The Hodge conjecture for powers of K3 surfaces

Abstract:

In this talk, after recalling the basics of Hodge theory, I will present some techniques that have proven to be effective in the study of the Hodge conjecture for powers of K3 surfaces. In particular, I will recall the construction of Kuga-Satake varieties starting from the second rational cohomology of a K3 surface and how it can be used to prove the Hodge conjecture for powers of K3 surfaces in some four-dimensional families. This talk is based on the paper [V].

[V] Varesco, M.: The Hodge conjecture for powers of K3 surfaces of Picard number 16. arXiv:2203.09778 (arXiv preprint) (2022)