中科院数学与系统科学研究院

数学研究所

代数几何研讨班

报告人：     郑志伟（清华丘成桐数学中心）

题  目：Orbifold Aspect of Certain Occult Period Maps

时  间：2017.12.25（星期一），11:00-12:00

地  点：数学院南楼N913室

摘  要：I will first introduce a vaiant of period map (the so-called occult period map) which associates certain projective manifolds (cubic surfaces, cubic threefolds, non-hyperelliptic curves of genus 3,4) with the Hodge structures of corresponding cyclic covers. Then I will talk about a uniform interpretation given by Rapoport and Kudla. I will give proof of some conjectures made by Rapoport and Kudla on orbifold aspects of those occult period maps. The proof go back to some basic technique in geometric invariant theory, and relies essentially on the known global torelli for cubic threefolds, cubic fourfolds, and K3 surfaces. See https://arxiv.org/abs/1711.02415.