K3 surfaces associated with varieties of generalized Kummer type

Floccari, Salvatore

doi:10.2140/gt.2026.30.1129

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K3 surfaces associated with varieties of generalized Kummer type

Salvatore Floccari

Geometry & Topology 30 (2026) 1129–1154

DOI: 10.2140/gt.2026.30.1129

Abstract

Any hyper-Kähler variety $K$ of generalized Kummer type is associated via Hodge theory with 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 and 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, strengthening a result of Markman.

Keywords

algebraic cycles, motives, Hodge conjecture, K3 surfaces, hyperkähler varieties

Mathematical Subject Classification

Primary: 14C15, 14C25, 14C30, 14J28, 14J42

References

Publication

Received: 18 January 2025

Revised: 12 July 2025

Accepted: 29 August 2025

Published: 20 April 2026

Proposed: Sándor J Kovács

Seconded: Marc Levine, Dan Abramovich

Authors

Salvatore Floccari
Fakültat für Mathematik Universität Bielefeld Bielefeld Germany	Institut für Mathematik Humboldt-Universität zu Berlin Berlin Germany

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Volume 30, issue 3 (2026)