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arXiv · 2607.16364

$0$-cycles and sheaves on abelian surfaces

Giovanni Mongardi·Gianluca Pacienza·Laura Pertusi
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Abstract

We introduce a filtration on the Chow ring of an abelian surface $A$, inspired by O'Grady's filtration on K3 surfaces. We give a geometric description of the filtration, and we prove that it is deeply linked with the rational orbit of points in the generalized Kummer variety of $A$. We propose a conjecture on the second Chern class of sheaves on this abelian surface, and we provide some evidence for the conjecture and prove some of its applications.

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Giovanni Mongardi, Gianluca Pacienza, Laura Pertusi. 2026-07-17. $0$-cycles and sheaves on abelian surfaces. https://arxiv.org/abs/2607.16364

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