Hermitian Variations of Hodge Structure of Calabi-Yau type

GAP Seminar

Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stiénon, Ping Xu.

Speaker: Radu Laza, Stony Brook University

Abstract: Except a few special cases (e.g. abelian varieties and K3 surfaces), the images of period maps for families of algebraic varieties satisfy non-trivial Griffiths' transversality relations. It is of interest to understand these images of period maps, especially for Calabi-Yau threefolds. In this talk, I will discuss the case when the images of period maps can be described algebraically. Specifically, I will show that if a horizontal subvariety Z of a period domain D is semi-algebraic and it is stabilized by a large discrete group, then Z is automatically a Hermitian symmetric domain with a totally geodesic embedding into the period domain D. I will then discuss the classification of the semi-algebraic cases for variations of Hodge structures of Calabi-Yau type, with a special emphasis on the classification over Q (which is partially based on earlier work of Zarhin). This is joint work with R. Friedman.

Room Reservation Information

Room Number: 106 McAllister

Date: 04/16/2013

Time: 2:30pm - 3:30pm