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Singularities and Complex Geometry
Edited by: Qi-keng Lu, Shantou University, Guangdong, People's Republic of China, and Stephen S.-T. Yau and Anatoly Libgober, University of Illinois at Chicago, IL
A co-publication of the AMS and International Press.
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AMS/IP Studies in Advanced Mathematics
1997; 342 pp; hardcover
Volume: 5
ISBN-10: 0-8218-0662-9
ISBN-13: 978-0-8218-0662-3
List Price: US$60
Member Price: US$48
Order Code: AMSIP/5
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This book represents the proceedings of the joint U.S.-China Seminar on Singularity and Complex Geometry held at the Institute of Mathematics of the Chinese Academy, Beijing, in June 1994. This was the first gathering of Chinese and American mathematicians working in these fields (several Japanese mathematicians also took part). The volume covers a wide range of problems in areas such as CR-manifolds, value distribution theory of holomorphic curves, topology of the complements of algebraic plane curves with singularities and arrangements, topology of non-isolated singularities, gauge theory on resolutions of simple singularities, and residues of foliations. The articles give accounts of research in these fast developing areas. Much of the material appears here for the first time in print.

Titles in this series are co-published with International Press, Cambridge, MA.

Readership

Graduate students, research mathematicians, physicists, and engineers interested in several complex variables and analytic spaces and algebraic geometry.

Table of Contents

  • J. Bland and C. L. Epstein -- Embeddable CR-structures and deformations of pseudoconvex surfaces
  • J. N. Damon -- Singular Milnor fibers and higher multiplicities for nonisolated complete intersections
  • K. Feng -- Non-congruent number, odd graph and the BSD conjecture \(Y^2 = X^3 - n^2X\)
  • E. Hironaka -- Multi-polynomial invariants for plane algebraic curves
  • S. Ishii -- The weighted blowing ups of singularities with \(\kappa = 0\)
  • G. Jiang and J. Feng -- An algorithm to produce the structure sequence of arrangement
  • T. Jiang and S. S.-T. Yau -- Complement of arrangement of hyperplanes
  • R. Kobayashi -- Value distribution theory of holomorphic curves into complex projective algebraic varieties and geometric Diophantine problems
  • A. Libgober -- The topology of complements to hypersurfaces and nonvanishing of a twisted deRham cohomology
  • Q. Lu -- The Horo-hypercircle coordinates and their application to the construction of a heat kernel
  • H. S. Luk and S. S.-T. Yau -- Complete algebraic CR invariants of real codimension 3 strongly pseudoconvex CR manifolds
  • H. Nakajima -- Gauge theory on resolutions of simple singularities and affine Lie algebras
  • A. Robb -- On branch curves of algebraic surfaces
  • H. Shi -- The Chern characters of surface with singularities
  • T. Suwa -- Residues of complex analytic foliations relative to singular invariant subvarieties
  • X.-J. Tan -- On \(H^0\)-lemma and projective normality of line bundles on algebraic curves
  • S. Wang -- A generalized Chern-Simons formulas
  • B. Wong -- On the singularity of the boundary of a convex domain admitting a non-compact automorphism group
  • J.-G. Yang -- Enumeration of combinations of rational double points on quartic surfaces
  • J. Yu -- Stokes regions of a simple singularity
  • Q. Yu, S. Gong, and X. Guo -- Schwarzian derivative of holomorphic mappings
  • Y. Yu -- Chern root algorithm and local index theorems
  • G. Zhang -- Notes on the codimensions of smooth map-germs and the related results
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