Geometry Seminar

University of Tor Vergata, Department of Mathematics

21st of March 2023, 14:30-15:30, room “Dal Passo”

Speaker

Salvatore Floccari

(Hannover)

Title

Sixfolds of generalized Kummer type and K3 surfaces

Abstract

The classical Kummer construction associates a K3 surface to

any 2-dimensional complex torus. I will present an analogue of this

construction in dimension six, which relates the two most studied

deformation types of hyper-Kähler manifolds in this dimension. Namely, I

will explain that any hyper-Kähler sixfold K of generalized Kummer type

has a naturally associated hyper-Kähler manifold of K3^[3]-type. If K is

projective then the associated K3^[3]-variety is a moduli space of

stable sheaves on a uniquely determined K3 surface, whose Picard rank is

that of K plus 15. I will also explain that the Kuga-Satake

correspondence for the K3 surfaces so obtained is induced by an

algebraic cycle, which gives infinitely many new families of K3 surfaces

of general Picard rank 16 for which the Kuga-Satake correspondence is

algebraic.