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On the group of zero-cycles of holomorphic symplectic varieties

Alina Marian, Xiaolei Zhao

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.

On the group of zero-cycles of holomorphic symplectic varieties

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.

Paper Structure

This paper contains 1 section, 3 theorems, 23 equations.

Table of Contents

  1. Acknowledgements

Key Result

Theorem 1

Let $X$ be a smooth projective K3 surface. For a primitive $v \in H^{\star} (X, \mathbb Z)$, and a $v$-generic stability condition $\sigma$, let $\mathsf M_\sigma (v)$ be the moduli space of $\sigma$-stable complexes on $X$ of Mukai vector $v$. Let $F_1$ and $F_2$ be two points in $\mathsf M_\sigma

Theorems & Definitions (6)

  • Theorem
  • Proposition
  • Lemma : markman, Lemma 4
  • Remark 1
  • Remark 2
  • Remark 3