Multiplier Ideal Sheaves in Algebraic and Complex Geometry

Abstract

The conference was organized by Joseph Kohn (Princeton), Georg Schumacher (Marburg), and Yum-Tong Siu (Harvard), and was attended by 44 participants. Its aim was to put together a group from both complex analysis and algebraic geometry, reflecting recent developments, where the title of the conference stands for phenomena and methods, closely related to both of these areas. The original approach involving the theory of partial differential equations and subelliptic estimates was addressed in several contributions, including estimates for the $\overline{\partial }$-Neumann problem, subelliptic PDE's and sub-Riemannian Geometry, and subelliptic estimates from an algebraic-geometric point of view. Main areas were also applications to the abundance conjecture, pseudoeffective bundles, and the use of the twisted Nakano identity to investigate the cohomology of multiplier ideals. Critical points of sections of holomorphic vector bundles were discussed from a probabilistic viewpoint. Concerning the hyperbolicity of complex manifolds, for entire analytic curves the multiplicity of the associated current with respect to subsets was studied, and holomorphic curves in semi-abelian varieties. Another main topic was recent results on invariants arising from multiplier ideal sheaves, and critical exponents of analytic functions related to jumping coefficients, applications to local analytic geometry, and also results concerning the Fujita conjecture. Finally recent progress on transcendental Morse inequalities was presented.