On the group of zero-cycles of holomorphic symplectic varieties

TL;DR

This paper proves that in certain moduli spaces of stable objects on K3 surfaces, the Chow class of a point is uniquely determined by the Chern class of the corresponding object, confirming a conjecture.

Contribution

It establishes that the Chow class of a point in these moduli spaces is determined by the Chern class, confirming a conjecture by Shen, Yin, and the second author.

Findings

Chow class of a point is determined by the Chern class

Confirms a conjecture on moduli spaces of stable objects

Provides a link between Chow classes and Chern classes in this context

Abstract

For a moduli space of Bridgeland-stable objects on a K3 surface, we show that the Chow class of a point is determined by the Chern class of the corresponding object on the surface. This establishes a conjecture of Junliang Shen, Qizheng Yin, and the second author.