0-cycles and sheaves on abelian surfaces

2026/07/17 by Giovanni Mongardi, Gianluca Pacienza, Laura Pertusi
#math.AG

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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.

Related

• Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady
• Algebraic cycles on a generalized Kummer variety
• Higher Chow Cycles on an Abelian Surface and a non-Archimedean analogue of the Hodge-D-conjecture
• A filtration on the higher Chow group of zero cycles on an abelian variety
• On the Chow group of zero-cycles of a generalized Kummer variety