Semi-algebraic horizontal subvarieties of Calabi-Yau type
Radu Laza, Stony Brook

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 is stabilized by a large discrete group, then Z is automatically Hermitian symmetric with a totally geodesic embedding into the period domain D. Additionally, I will discuss the classification of the semi-algebraic cases for variations of Hodge structures of Calabi-Yau type. This is joint work with R. Friedman.