中国科学院数学与系统科学研究院

数学研究所

学术报告

多复变与复几何研讨班

SCV&CG Seminar

Speaker: Prof. Takeo Ohsawa (Nagoya University)

Inviter: 周向宇 院士

Language: English

Title: A note on the contraction problem

Time&Venue: 2025年5月6日（星期二） 19:00 - 20:00 & 南楼N913

Abstract: It is well known that a connected compact complex submanifold of a complex manifold M is contractible to a point if the normal bundle is negative. It was proved by Grauert in 1962. On the other hand, it is sometimes misunderstood (Shepherd-Barron's paper in 1983) that its relative version is correct, although there is a counterexample written in Fujiki's thesis in 1975. It will be reported that nevertheless one can show a contraction theorem, not to subspaces of Stein spaces but to a compact manifold with negative or positive canonical bundle. It is an application of a generalization of Grauert's finiteness theorem in 1958.