Singularities and Complex Geometry

by Lu, Qi-Keng; Yau, Stephen Shing-Toung; Libgober, Anatoly

• ISBN13: 9780821806623
• ISBN10: 0821806629
• Format: Hardcover
• Copyright: 1997-02-01
• Publisher: Amer Mathematical Society

Summary

This book presents 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, USA.

Table of Contents

Embeddable CR-structures and deformations of pseudoconvex surfaces

Singular Milnor fibers and higher multiplicities for nonisolated complete intersections

Non-congruent number, odd graph and the BSD conjecture $Y^2 = X^3 - n^2X$

Multi-polynomial invariants for plane algebraic curves

The weighted blowing ups of singularities with $\kappa = 0$

An algorithm to produce the structure sequence of arrangement

Complement of arrangement of hyperplanes

Value distribution theory of holomorphic curves into complex projective algebraic varieties and geometric Diophantine problems

The topology of complements to hypersurfaces and nonvanishing of a twisted deRham cohomology

The Horo-hypercircle coordinates and their application to the construction of a heat kernel

Complete algebraic CR invariants of real codimension 3 strongly pseudoconvex CR manifolds

Gauge theory on resolutions of simple singularities and affine Lie algebras

On branch curves of algebraic surfaces

The Chern characters of surface with singularities

Residues of complex analytic foliations relative to singular invariant subvarieties

On $H^0$-lemma and projective normality of line bundles on algebraic curves

A generalized Chern-Simons formulas

On the singularity of the boundary of a convex domain admitting a non-compact automorphism group

Enumeration of combinations of rational double points on quartic surfaces

Stokes regions of a simple singularity

Schwarzian derivative of holomorphic mappings

Chern root algorithm and local index theorems

Notes on the codimensions of smooth map-germs and the related results

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