中科院数学与系统科学研究院

数学研究所

微分几何讨论班

报告人：Prof. Ping Li（Tongji University） 

题  目：Nonnegative hermitian holomorphic vector bundles and Chern numbers

时  间：2018.03.15（星期四），10 :00-11:00

地  点：数学院南楼N913室

摘  要：If a holomorphic vector bundle on a compact complex manifold has a nonnegative curvature Hermitian metric in the sense of Bott and Chern, which always exists on globally generated holomorphic vector bundles, then some special linear combinations of Chern forms w.r.t. the Chern connection are nonnegative. This particularly implies that all the Chern numbers of such a holomorphic vector bundle are nonnegative and can be bounded below and above respectively by two special Chern numbers in an explicit manner. As applications, we obtain a family of new results on compact complex manifolds whose holomorphic tangent or cotangent bundles are globally generated, some of which improve several classical results. This talk is based on the speaker's preprint, which is available at https://arxiv.org/abs/1702.01701