Algebraic Geometry Seminar: "Recent progress on Hodge loci"

Speaker: Bruno Klingler, Humboldt University, Berlin

Abstract: Given a smooth family of projective varieties on a quasi projective base S, its Hodge locus is the set of closed points of S where the fiber admits "exceptional" Hodge classes. In 1995 Cattani, Deligne and Kaplan showed that it is a countable union of algebraic subvarieties of S, as predicted by the Hodge conjecture. In this talk I will discuss the recent progress in understanding the geometry and arithmetic of the Hodge locus: in "most cases" it is actually algebraic (rather than a countable union of algebraic subvarieties of S), defined over a number field if the family is. Based on works of Baldi-Klingler-Ullmo, Klingler-Otwinowska-Urbanik, Kreutz.

Host: Matt Kerr