**AMS/IP Studies in Advanced Mathematics**

Volume: 5;
1997;
342 pp;
Hardcover

MSC: Primary 14; 16; 32; 53; 57; 58;

Print ISBN: 978-0-8218-0662-3

Product Code: AMSIP/5

List Price: $63.00

AMS Member Price: $50.40

MAA Member Price: $56.70

**Electronic ISBN: 978-1-4704-3796-1
Product Code: AMSIP/5.E**

List Price: $63.00

AMS Member Price: $50.40

MAA Member Price: $56.70

# Singularities and Complex Geometry

Share this page *Edited by *
*Qi-keng Lu; Stephen S.-T. Yau; Anatoly Libgober*

A co-publication of the AMS and International Press of Boston

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 of Boston, Inc., Cambridge, MA.

#### Readership

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

# Table of Contents

## Singularities and Complex Geometry

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- List of participants ix10
- Embeddable CR-structures and deformations of pseudoconvex surfaces 112
- Singular Milnor fibers and higher multiplicities for nonisolated complete intersections 2839
- Non-congruent number, odd graph and the BSD conjecture 𝑦²=𝑥³-𝑛²𝑥 5465
- Multi-polynomial invariants for plane algebraic curves 6778
- The weighted blowing ups of singularities with 𝜅=0 7586
- An algorithm to produce the structure sequence of arrangement 8394
- Complement of arrangement of hyperplanes 93104
- Value distribution theory of holomorphic curves into complex projective algebraic varieties and geometric Diophantine problems 105116
- The topology of complements to hypersurfaces and nonvanishing of a twisted deRham cohomology 116127
- The horo-hypercircle coordinates and their application to the construction of a heat kernel 131142
- Complete algebraic CR invariants of real codimension 3 strongly pseudoconvex CR manifolds 175186
- Gauge theory on resolutions of simple singularities and affine Lie algebras 183194
- On branch curves of algebraic surfaces 193204
- The Chern characters of surface with singularities 222233
- Residues of complex analytic foliations relative to singular invariant subvarieties 230241
- On 𝐻⁰-lemma and projective normality of line bundles on algebraic curves 246257
- A generalized Chern-Simons formulas 255266
- On the singularity of the boundary of a convex domain admitting a non-compact automorphism group 265276
- Enumeration of combinations of rational double points on quartic surfaces 275286
- Stokes regions of a simple singularity 313324
- Schwarzian derivative of holomorphic mappings 317328
- Chern root algorithm and local index theorems 324335
- Notes on the codimensions of smooth map-germs and the related results 334345
- Back Cover Back Cover1354