K3 surfaces associated with varieties of generalized Kummer type
Abstract
With any hyper-Kähler variety $K$ of generalized Kummer type is associated via Hodge theory a K3 surface $S_K$. We show how they are related geometrically through a moduli space of sheaves on $S_K$. As a consequence, building fundamentally on the works of O'Grady, Markman, Voisin, Varesco, we establish the Hodge conjecture for all powers of any of these K3 surfaces as well as for all abelian fourfolds of Weil type with discriminant 1 and their powers, strenghtening a result of Markman.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Advanced Algebra and Geometry
Publication details
- Journal / source
- Geometry & Topology
- Volume
- 30
- Issue
- 3
- Pages
- 1129–1154
- Publication date
- 20 April 2026
- Language
- EN