多复变与复几何学术活动

中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

多复变与复几何学术活动

Some Topics in Several Complex Variables

报告人：曹俊彦    教授(Université Côte d'Azur)

题  目：On extension of pluricanonical forms of a Kähler family and a curvature formula for the positivity of direct images

时  间：第一讲：4月 7 日 19:30-21:30第二讲：4月14日 18:30-20:30第三讲：4月21日 19:30-21:30

地  点：腾讯会议 (统一密码：2021)会议号1：351 427 796会议号2：770 562 930会议号3：236 635 971

摘  要：We will explain some recent results related to the direct images of relative (pluri)-canonical bundle.

Lecture 1:

We will first recall briefly the classical results of Bo Berndtsson about the positivity of direct images and the invariance of plurigenre in the projective case.

Lecture 2:

In the second part, we will explain a curvature formula for the direct images of twisted relative canonical bundle in the case when the metric might be singular. It can be seen as a generalization of Bo Berndtsson's theory. It is a joint work with Henri Guenancia and Mihai Paun.

Lecture 3:

In the third part, we will explain an analytic approche to extend the pluricanonical forms on the central fiber of a smooth compact Kähler family under the assumption that the pluricanonical form is not very singular. It is a joint work with Mihai Paun.