On the Zariski closure of the positive dimensional Hodge locus
HARVARD-MIT ALGEBRAIC GEOMETRY
Bruno Klingler - Humboldt University, Berlin
Given a variation of Hodge structures $V$ on a smooth complex quasi-projective variety $S$, its Hodge locus is the set of points $s$ in $S$ where the Hodge structure $V_s$ admits exceptional Hodge tensors. A famous result of Cattani, Deligne and Kaplan shows that this Hodge locus is a countable union of irreducible algebraic subvarieties of $S$, called the special subvarieties of $(S, V)$. In this talk I will discuss the geometry of the Zariski closure of the union of the positive dimensional special subvarieties. This is joint work with Ania Otwinowska.