Westlake Online Math Forum第十八期 | Junyan Cao: On Extension of Twisted Canonical forms

2024-04-07 08:28:38



ZOOM ID:989 5547 3545

PASSCODE: 416134

主持人: Xin Fu, Institute for Theoretical Sciences

主讲人: Junyan Cao,Université Côte D'Azur, Laboratoire J.A. Dieudonné

主讲人介绍: Professor Cao is now a professor at Université Côte D'Azur, Laboratoire J.A. Dieudonné. His research interest focuses on complex algebraic geometry. He has made many great contributions to several classical problems including Itaka conjecture, extension problem etc.

讲座主题:On Extension of Twisted Canonical forms


In complex geometry, we are interested in how to extend a holomorphic section on a subvariety to the total space. One important result in this direction is due to Y.-T. Siu, who shows the invariance of plurigenera for a projective family. The invariance of plurigenera in the Kähler setting is still open. In this talk, we will present some results concerning the lifting of twisted canonical sections defined on an infinitesimal neighborhood of the central fiber of a smooth, proper Kähler family, which verify a natural L2 condition. We obtain a few results in connection with the invariance of plurigenera for Kähler families.