Generalized Franchetta conjecture for certain families of K3 surfaces and hyper-Kähler varieties

Abstract: In 2013, as an analogue of Franchetta's classical conjecture on the Picard group of the universal genus g curve, O'Grady asked whether the Chow group of zero-cycles of the generic fiber of the universal genus-g K3 surface is cyclic. I will discuss some recent progress that I obtained in collaboration with Laterveer and Vial on this conjecture as well as its higher dimensional version for hyper-Kähler varieties. The main feature of our argument is the combination of the projective geometry of cubic fourfolds on one hand and moduli spaces of Bridgeland stable objects in their Kuznetsov components on the other hand.

algebraic geometry

Audience: researchers in the topic

Derived seminar

Series comments: https://ed-ac-uk.zoom.us/j/89993982042

Password: a simply-connected two-dimensional variety with trivial canonical bundle (omit the space)