Global deformation of polarized varieties
HTML articles powered by AMS MathViewer
- by T. Matsusaka PDF
- Bull. Amer. Math. Soc. 80 (1974), 1-7
References
- M. Artin, The implicit function theorem in algebraic geometry, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968) Oxford Univ. Press, London, 1969, pp. 13–34. MR 0262237
- Walter L. Baily Jr., On the moduli of Jacobian varieties, Ann. of Math. (2) 71 (1960), 303–314. MR 110715, DOI 10.2307/1970084
- Walter L. Baily Jr., On the theory of $\theta$-functions, the moduli of abelian varieties, and the moduli of curves, Ann. of Math. (2) 75 (1962), 342–381. MR 162799, DOI 10.2307/1970178
- Wei-Liang Chow and B. L. van der Waerden, Zur algebraischen Geometrie. IX, Math. Ann. 113 (1937), no. 1, 692–704 (German). MR 1513117, DOI 10.1007/BF01571660 5. A. Grothendieck and J. Dieudonné, Éléments de géometrie algébriques, Inst. Hautes Études Sci. Publ. Math. (1960 ff)
- K. Kodaira, On a differential-geometric method in the theory of analytic stacks, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 1268–1273. MR 66693, DOI 10.1073/pnas.39.12.1268
- K. Kodaira and D. C. Spencer, On deformations of complex analytic structures. I, II, Ann. of Math. (2) 67 (1958), 328–466. MR 112154, DOI 10.2307/1970009
- Solomon Lefschetz, On certain numerical invariants of algebraic varieties with application to abelian varieties, Trans. Amer. Math. Soc. 22 (1921), no. 3, 327–406. MR 1501178, DOI 10.1090/S0002-9947-1921-1501178-3
- Teruhisa Matsusaka, Theory of $Q$-varieties, Mathematical Society of Japan, Tokyo, 1964. MR 0186673
- T. Matsusaka, Polarized varieties, fields of moduli and generalized Kummer varieties of polarized abelian varieties, Amer. J. Math. 80 (1958), 45–82. MR 94360, DOI 10.2307/2372821
- T. Matsusaka, Algebraic deformations of polarized varieties, Nagoya Math. J. 31 (1968), 185–245; corrections, ibid. 33 (1968), 137; 36 (1968), 119. MR 258827, DOI 10.1017/s0027763000013167
- T. Matsusaka, On canonically polarized varieties, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968) Oxford Univ. Press, London, 1969, pp. 265–306. MR 0263815
- T. Matsusaka, Polarized varieties with a given Hilbert polynomial, Amer. J. Math. 94 (1972), 1027–1077. MR 337960, DOI 10.2307/2373563
- T. Matsusaka and D. Mumford, Two fundamental theorems on deformations of polarized varieties, Amer. J. Math. 86 (1964), 668–684. MR 171778, DOI 10.2307/2373030
- D. Mumford, Pathologies. III, Amer. J. Math. 89 (1967), 94–104. MR 217091, DOI 10.2307/2373099
- Ichiro Satake, On the compactification of the Siegel space, J. Indian Math. Soc. (N.S.) 20 (1956), 259–281. MR 84842
- Jean-Pierre Serre, Un théorème de dualité, Comment. Math. Helv. 29 (1955), 9–26 (French). MR 67489, DOI 10.1007/BF02564268
- Carl Ludwig Siegel, Gesammelte Abhandlungen. Bände I, II, III, Springer-Verlag, Berlin-New York, 1966 (German). Herausgegeben von K. Chandrasekharan und H. Maass. MR 0197270
- André Weil, Foundations of algebraic geometry, American Mathematical Society, Providence, R.I., 1962. MR 0144898
Additional Information
- Journal: Bull. Amer. Math. Soc. 80 (1974), 1-7
- MSC (1970): Primary 14-02, 14D15, 14D20, 14E25
- DOI: https://doi.org/10.1090/S0002-9904-1974-13340-9
- MathSciNet review: 0364246