$0$-cycles and sheaves on abelian surfaces

Giovanni Mongardi; Gianluca Pacienza; Laura Pertusi

$0$-cycles and sheaves on abelian surfaces

Algebraic Geometry 2026-07-17 v1

Authors: Giovanni Mongardi , Gianluca Pacienza , Laura Pertusi

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.

Keywords

abelian surfaces Chow ring filtration O'Grady filtration generalized Kummer variety second Chern class sheaves

Cite

@article{arxiv.2607.16364,
  title  = {$0$-cycles and sheaves on abelian surfaces},
  author = {Giovanni Mongardi and Gianluca Pacienza and Laura Pertusi},
  journal= {arXiv preprint arXiv:2607.16364},
  year   = {2026}
}