【时间】
2024.12.16-2024.12.19 9:00-11:30am
【摘要】
In this intensive course, I will explain recent developments of the positivity of direct image sheaves of adjoint bundles from the viewpoint of complex geometry and their applications to algebraic geometry. I will first introduce the analytic Griffiths positivity of direct image sheaves as a beautiful application of the Ohsawa-Takegoshi L2 extension theorem and discuss our attempt to generalize the Griffiths positivity to the Nakano positivity. Furthermore, I will present some applications to algebraic geometry and discuss related open problems.
I will begin by reviewing fundamental notions in complex geometry, including the definition of Hermitian metrics, Chern connections, and curvatures on vector bundles, ensuring that many students (including undergraduate students) and postdocs can participate in this intensive course.
