# Journées de Géométrie Algébrique Poitiers-Bordeaux

24-25 November 2016
Poitiers
Europe/Paris timezone

## Isogenies and transcendental Hodge structures of K3 surfaces

24 Nov 2016, 16:15
50m
0-6 (Poitiers)

Board: 9
Exposé de 50 min

### Speaker

Prof. Samuel Boissière

### Description

Every Hodge class on a product of two complex projective K3 surfaces induces a homomorphism of rational Hodge structures between the respective transcendental lattices. Under the hypothesis that this morphism is an isometry of rational quadratic spaces, Mukai, Nikulin and recently Buskin have proven that the corresponding Hodge class is algebraic, confirming the Hodge conjecture in this context. In this talk, I will show that the hypothesis of isometry is too restrictive by constructing geometrically some families of isogenies between K3 surfaces whose transcendental Hodge structures are nonisometric. This is a collaboration with Alessandra Sarti and Davide Cesera Veniani.

### Presentation Materials

There are no materials yet.