题目：Extensions of holomorphic forms
报告人：杨瑞杰（Stony Brook University）
摘要：Given a family of n-dimensional complex projective manifolds over a base B, the spaces of top holomorphic differential forms (i.e. (n,0) forms) on fibers give rise to a holomorphic vector bundle H on B which is equipped with a positive metric. Ohsawa-Takegoshi theorem with sharp estimates, recently proved by Blocki and Guan-Zhou, implies that one can extend top forms on the central fiber with good L2 bounds. This analytic input only guarantees the existence of extensions. I would like to discuss a project in progress about geometric approaches to this problem for certain families. The main tool is Griffiths’ theory of variation of Hodge structures and the corresponding Deligne’s representation-theoretic interpretation. The necessary background will be reviewed in the first part of the talk.