Seminario Geometría

Hodge theory of abelian covers of algebraic varieties

Ponente:  Moisés Herradón Cueto (UAM)
Fecha:  jueves 30 de marzo de 2023 - 12:00
Lugar:  Aula Naranja, ICMAT


Let f \colon U\to \mathbb C^* be an algebraic map from a smooth complex connected algebraic variety U to the punctured complex line \mathbb C^*. Using f to pull back the exponential map \mathbb C\to \mathbb C^*, one obtains an infinite cyclic cover U^f of the variety U, together with a \mathbb Z-action coming from adding 2\pi i in \mathbb C. The homology groups of this infinite cyclic cover, with their \mathbb Z-actions, are the family of Alexander modules associated to f. In previous work jointly with Eva Elduque, Christian Geske, Laurențiu Maxim and Botong Wang, we constructed a mixed Hodge structure (MHS) on the torsion part of these Alexander modules. In this talk, we will talk about work in progress aimed at generalizing this theory to abelian covering spaces of algebraic varieties which arise in an algebraic way, i.e. from maps f \colon U \to G, where G is a semiabelian variety. This is joint work with Eva Elduque.