代数几何研讨班:Cyclic covering construction and the vanishing theorem

报告人：Prof. Kang Zuo （Universit？t Mainz）

题  目：Cyclic covering construction and the vanishing theorem

时  间：2019.08.26（星期一）, 9:30-11:30

地  点：数学院南楼N902

摘  要： In this lecture we first give a review to the cyclic covering construction. Then we construct a comparison map between the cohomology group of some wedge product of the tangent sheaf and some Hogde cohomology group of certain local system. This can be viewed as the absolute version of the Viehweg-Zuo’s construction.

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报告人：Prof. Kang Zuo （Universit？t Mainz）

题  目：Iterated Kodaira-Spencer maps and the construction of Viehweg-Zuo sheaves

时  间：2019.08.26（星期一）, 15:30-17:30

地  点：数学院南楼N902

摘  要： In this lecture we first introduce the generalized Kodaira-Spencer maps for a given family. By using those maps we construct a Higgs bundle associated to the family. Then we explain how to use this Higgs bundle and the cyclic covering to find a big subsheaf in some symmetric power of the cotangent sheaf of the base space of the family, which is called the Viehweg-Zuo sheaf now.

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报告人：Prof. Kang Zuo（Universit？t Mainz）

题  目：Boundedness and Rigidity of family of polarized varieties

时  间：2019.08.28（星期三）, 9:30-11:30

地  点：数学院南楼N902

摘  要：In this lecture, we shall talk about some questions in the Shafarevich program for higher dimensional case by using the construction presented in previous lectures.  We will prove the boundedness property and give a criteria for the rigidity of the given family.