报告题目： On The Geometry of Smooth Toroidal Compactifications of Siegel Varieties I & II

报告人：  张毅教授   复旦大学

报告时间： 2013年6月20日 （星期四） 14：30-16:00pm ,
                 2013年6月27日 （星期四） 14：30-16:00pm
 
报告地点：管理科研楼1218教室

报告摘要：

This work is a part of  joint program with S.-T. Yau. We study smooth toroidal compactifications of Siegel varieties thoroughly from the viewpoints of Hodge theory and K/"ahler-Einstein metric..
We observe that any cusp of a Siegel space can be identified as a set of certain weight one polarized mixed Hodge structures.We then study the infinity boundary divisors of toroidalcompactifications, and obtain a global volume form formula of an arbitrary smooth Siegel variety $/sA_{g,/Gamma}(g>1)$ with a smooth toroidal compactification $/overline{/sA}_{g,/Gamma}$ such that $D_/infty:=/overline{/sA}_{g,/Gamma}/setminus /sA_{g,/Gamma}$ is normal crossing. We use this volume form formula to show that the unique group-invariant K/"ahler-Einstein metric on $/sA_{g,/Gamma}$ endows some restraint combinatorial conditions for all smooth toroidalcompactifications of $/sA_{g,/Gamma}.$  Again using the volume form formula, we study the asymptotic behaviour of logarithmical canonical line bundle on any smooth toroidal compactification of $/sA_{g,/Gamma}$ carefully and we obtain that the logarithmical canonical bundle degenerate sharply even though it is big and numerically effective.

主办单位: 中国科学技术大学数学科学学院        中科院吴文俊数学重点实验室

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