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