K3 surfaces associated with varieties of generalized Kummer type

2025/01/04 by Floccari, Salvatore · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.02315

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.

Cited by

• Coble duality for Jacobian Kummer fourfolds

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