14-XX |
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Algebraic geometry |
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14-00 |
General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to algebraic geometry |
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14-01 |
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry |
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14-02 |
Research exposition (monographs, survey articles) pertaining to algebraic geometry |
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14-03 |
History of algebraic geometry [Consider also classification numbers from Section 01-XX] |
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14-04 |
Software, source code, etc. for problems pertaining to algebraic geometry |
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14-06 |
Proceedings, conferences, collections, etc. pertaining to algebraic geometry |
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14-11 |
Research data for problems pertaining to algebraic geometry |
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14A05 |
Relevant commutative algebra [See also 13-XX] |
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14A10 |
Varieties and morphisms |
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14A15 |
Schemes and morphisms |
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14A20 |
Generalizations (algebraic spaces, stacks) |
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14A21 |
Logarithmic algebraic geometry, log schemes |
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14A22 |
Noncommutative algebraic geometry [See also 16S38] |
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14A23 |
Geometry over the field with one element |
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14A25 |
Elementary questions in algebraic geometry |
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14A30 |
Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) {For categorical aspects, see 18Fxx, 18Gxx} |
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14A99 |
None of the above, but in this section |
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14B05 |
Singularities in algebraic geometry [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] |
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14B07 |
Deformations of singularities [See also 14D15, 32S30] |
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14B10 |
Infinitesimal methods in algebraic geometry [See also 13D10] |
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14B12 |
Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10] |
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14B15 |
Local cohomology and algebraic geometry [See also 13D45, 32C36] |
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14B20 |
Formal neighborhoods in algebraic geometry |
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14B25 |
Local structure of morphisms in algebraic geometry: étale, flat, etc. [See also 13B40] |
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14B99 |
None of the above, but in this section |
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14C05 |
Parametrization (Chow and Hilbert schemes) |
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14C15 |
(Equivariant) Chow groups and rings; motives |
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14C17 |
Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry [See also 13H15] |
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14C20 |
Divisors, linear systems, invertible sheaves |
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14C21 |
Pencils, nets, webs in algebraic geometry [See also 53A60] |
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14C22 |
Picard groups |
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14C25 |
Algebraic cycles |
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14C30 |
Transcendental methods, Hodge theory (algebro-geometric aspects) [See also 14D07, 32G20, 32J25, 32S35, 58A14], Hodge conjecture |
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14C34 |
Torelli problem [See also 32G20] |
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14C35 |
Applications of methods of algebraic $K$-theory in algebraic geometry [See also 19Exx] |
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14C40 |
Riemann-Roch theorems [See also 19E20, 19L10] |
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14C99 |
None of the above, but in this section |
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14D05 |
Structure of families (Picard-Lefschetz, monodromy, etc.) |
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14D06 |
Fibrations, degenerations in algebraic geometry |
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14D07 |
Variation of Hodge structures (algebro-geometric aspects) [See also 32G20] |
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14D10 |
Arithmetic ground fields (finite, local, global) and families or fibrations |
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14D15 |
Formal methods and deformations in algebraic geometry [See also 13D10, 14B07, 32Gxx] |
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14D20 |
Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} |
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14D21 |
Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) [See also 32L25, 81Txx] |
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14D22 |
Fine and coarse moduli spaces |
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14D23 |
Stacks and moduli problems |
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14D24 |
Geometric Langlands program (algebro-geometric aspects) [See also 22E57] |
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14D99 |
None of the above, but in this section |
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14E05 |
Rational and birational maps |
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14E07 |
Birational automorphisms, Cremona group and generalizations |
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14E08 |
Rationality questions in algebraic geometry [See also 14M20] |
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14E15 |
Global theory and resolution of singularities (algebro-geometric aspects) [See also 14B05, 32S20, 32S45] |
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14E16 |
McKay correspondence |
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14E18 |
Arcs and motivic integration |
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14E20 |
Coverings in algebraic geometry [See also 14H30] |
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14E22 |
Ramification problems in algebraic geometry [See also 11S15] |
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14E25 |
Embeddings in algebraic geometry |
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14E30 |
Minimal model program (Mori theory, extremal rays) |
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14E99 |
None of the above, but in this section |
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14F06 |
Sheaves in algebraic geometry [See also 14F08, 14H60, 14J60, 18F20, 32L10, 46M20] |
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14F08 |
Derived categories of sheaves, dg categories, and related constructions in algebraic geometry [See also 14A30, 14F06, 18Gxx] |
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14F10 |
Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38] |
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14F17 |
Vanishing theorems in algebraic geometry [See also 32L20] |
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14F18 |
Multiplier ideals |
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14F20 |
Étale and other Grothendieck topologies and (co)homologies |
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14F22 |
Brauer groups of schemes [See also 12G05, 16K50] |
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14F25 |
Classical real and complex (co)homology in algebraic geometry |
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14F30 |
$p$-adic cohomology, crystalline cohomology |
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14F35 |
Homotopy theory and fundamental groups in algebraic geometry [See also 14H30] |
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14F40 |
de Rham cohomology and algebraic geometry [See also 14C30, 32C35, 32L10] |
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14F42 |
Motivic cohomology; motivic homotopy theory [See also 19E15] |
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14F43 |
Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) |
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14F45 |
Topological properties in algebraic geometry |
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14F99 |
None of the above, but in this section |
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14G05 |
Rational points |
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14G10 |
Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) [See also 11G40] |
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14G12 |
Hasse principle, weak and strong approximation, Brauer-Manin obstruction [See also 14F22] |
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14G15 |
Finite ground fields in algebraic geometry |
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14G17 |
Positive characteristic ground fields in algebraic geometry |
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14G20 |
Local ground fields in algebraic geometry |
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14G22 |
Rigid analytic geometry |
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14G25 |
Global ground fields in algebraic geometry |
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14G27 |
Other nonalgebraically closed ground fields in algebraic geometry |
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14G32 |
Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) |
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14G35 |
Modular and Shimura varieties [See also 11F41, 11F46, 11G18] |
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14G40 |
Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30] |
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14G45 |
Perfectoid spaces and mixed characteristic |
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14G50 |
Applications to coding theory and cryptography of arithmetic geometry [See also 94A60, 94B27, 94B40] |
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14G99 |
None of the above, but in this section |
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14H05 |
Algebraic functions and function fields in algebraic geometry [See also 11R58] |
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14H10 |
Families, moduli of curves (algebraic) |
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14H15 |
Families, moduli of curves (analytic) [See also 30F10, 32G15] |
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14H20 |
Singularities of curves, local rings [See also 13Hxx, 14B05] |
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14H25 |
Arithmetic ground fields for curves [See also 11Dxx, 11G05, 14Gxx] |
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14H30 |
Coverings of curves, fundamental group [See also 14E20, 14F35] |
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14H37 |
Automorphisms of curves |
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14H40 |
Jacobians, Prym varieties [See also 32G20] |
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14H42 |
Theta functions and curves; Schottky problem [See also 14K25, 32G20] |
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14H45 |
Special algebraic curves and curves of low genus |
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14H50 |
Plane and space curves |
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14H51 |
Special divisors on curves (gonality, Brill-Noether theory) |
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14H52 |
Elliptic curves [See also 11G05, 11G07, 14Kxx] |
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14H55 |
Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx] |
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14H57 |
Dessins d'enfants theory {For arithmetic aspects, see 11G32} |
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14H60 |
Vector bundles on curves and their moduli [See also 14D20, 14F06, 14J60] |
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14H70 |
Relationships between algebraic curves and integrable systems |
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14H81 |
Relationships between algebraic curves and physics |
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14H99 |
None of the above, but in this section |
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14J10 |
Families, moduli, classification: algebraic theory |
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14J15 |
Moduli, classification: analytic theory; relations with modular forms [See also 32G13] |
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14J17 |
Singularities of surfaces or higher-dimensional varieties [See also 14B05, 14E15, 32S05, 32S25] |
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14J20 |
Arithmetic ground fields for surfaces or higher-dimensional varieties [See also 11Dxx, 11G25, 11G35, 14Gxx] |
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14J25 |
Special surfaces {For Hilbert modular surfaces, see 14G35} |
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14J26 |
Rational and ruled surfaces |
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14J27 |
Elliptic surfaces, elliptic or Calabi-Yau fibrations |
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14J28 |
$K3$ surfaces and Enriques surfaces |
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14J29 |
Surfaces of general type |
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14J30 |
$3$-folds |
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14J32 |
Calabi-Yau manifolds (algebro-geometric aspects) [See also 32Q25] |
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14J33 |
Mirror symmetry (algebro-geometric aspects) [See also 11G42, 53D37] |
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14J35 |
$4$-folds |
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14J40 |
$n$-folds ($n>4$) |
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14J42 |
Holomorphic symplectic varieties, hyper-Kähler varieties |
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14J45 |
Fano varieties |
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14J50 |
Automorphisms of surfaces and higher-dimensional varieties |
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14J60 |
Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F06, 14H60, 32Lxx] |
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14J70 |
Hypersurfaces and algebraic geometry |
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14J80 |
Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) |
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14J81 |
Relationships between surfaces, higher-dimensional varieties, and physics |
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14J99 |
None of the above, but in this section |
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14K02 |
Isogeny |
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14K05 |
Algebraic theory of abelian varieties |
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14K10 |
Algebraic moduli of abelian varieties, classification [See also 11G15] |
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14K12 |
Subvarieties of abelian varieties |
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14K15 |
Arithmetic ground fields for abelian varieties [See also 11Dxx, 11Fxx, 11G10, 14Gxx] |
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14K20 |
Analytic theory of abelian varieties; abelian integrals and differentials |
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14K22 |
Complex multiplication and abelian varieties [See also 11G15] |
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14K25 |
Theta functions and abelian varieties [See also 14H42] |
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14K30 |
Picard schemes, higher Jacobians [See also 14H40, 32G20] |
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14K99 |
None of the above, but in this section |
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14L05 |
Formal groups, $p$-divisible groups [See also 55N22] |
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14L10 |
Group varieties |
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14L15 |
Group schemes |
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14L17 |
Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18C40] |
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14L24 |
Geometric invariant theory [See also 13A50] |
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14L30 |
Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] |
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14L35 |
Classical groups (algebro-geometric aspects) [See also 20Gxx, 51N30] |
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14L40 |
Other algebraic groups (geometric aspects) |
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14L99 |
None of the above, but in this section |
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14M05 |
Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10] |
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14M06 |
Linkage [See also 13C40] |
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14M07 |
Low codimension problems in algebraic geometry |
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14M10 |
Complete intersections [See also 13C40] |
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14M12 |
Determinantal varieties [See also 13C40] |
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14M15 |
Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] |
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14M17 |
Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15] |
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14M20 |
Rational and unirational varieties [See also 14E08] |
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14M22 |
Rationally connected varieties |
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14M25 |
Toric varieties, Newton polyhedra, Okounkov bodies [See also 52B20] |
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14M27 |
Compactifications; symmetric and spherical varieties |
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14M30 |
Supervarieties [See also 32C11, 58A50] |
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14M35 |
Character varieties |
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14M99 |
None of the above, but in this section |
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14N05 |
Projective techniques in algebraic geometry [See also 51N35] |
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14N07 |
Secant varieties, tensor rank, varieties of sums of powers |
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14N10 |
Enumerative problems (combinatorial problems) in algebraic geometry |
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14N15 |
Classical problems, Schubert calculus |
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14N20 |
Configurations and arrangements of linear subspaces |
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14N25 |
Varieties of low degree |
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14N30 |
Adjunction problems |
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14N35 |
Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) [See also 53D45] |
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14N99 |
None of the above, but in this section |
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14P05 |
Real algebraic sets [See also 12D15, 13J30] |
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14P10 |
Semialgebraic sets and related spaces |
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14P15 |
Real-analytic and semi-analytic sets [See also 32B20, 32C05] |
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14P20 |
Nash functions and manifolds [See also 32C07, 58A07] |
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14P25 |
Topology of real algebraic varieties |
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14P99 |
None of the above, but in this section |
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14Q05 |
Computational aspects of algebraic curves [See also 14Hxx] |
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14Q10 |
Computational aspects of algebraic surfaces [See also 14Jxx] |
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14Q15 |
Computational aspects of higher-dimensional varieties [See also 14Jxx, 14Mxx] |
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14Q20 |
Effectivity, complexity and computational aspects of algebraic geometry |
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14Q25 |
Computational algebraic geometry over arithmetic ground fields [See also 14Gxx, 14H25, 14Kxx] |
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14Q30 |
Computational real algebraic geometry [See also 14Pxx] |
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14Q65 |
Geometric aspects of numerical algebraic geometry [See also 65H14] |
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14Q99 |
None of the above, but in this section |
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14R05 |
Classification of affine varieties |
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14R10 |
Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) |
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14R15 |
Jacobian problem [See also 13F20] |
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14R20 |
Group actions on affine varieties [See also 13A50, 14L30] |
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14R25 |
Affine fibrations [See also 14D06] |
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14R99 |
None of the above, but in this section |
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14T10 |
Foundations of tropical geometry and relations with algebra {For algebraic aspects, see 15A80} |
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14T15 |
Combinatorial aspects of tropical varieties |
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14T20 |
Geometric aspects of tropical varieties |
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14T25 |
Arithmetic aspects of tropical varieties |
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14T90 |
Applications of tropical geometry |
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14T99 |
None of the above, but in this section |