Filtrations on the derived category of twisted K3 surfaces

2024/02/21 by Chen, Zaiyuan, Li, Zhiyuan, Zhang, Ruxuan +1
#14C25 #14F08 #14J28 #14J42 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.13793

Abstract

We introduce and study the Shen-Yin-Zhao filtration on derived categories of twisted K3 surfaces. A main contribution is the construction of a twisted Beauville-Voisin class \mathfrako_\mathscrX ∈ CH₀(X) that extends fundamental results of O'Grady and Shen-Yin-Zhao \citeOG13, SYZ20 to twisted settings. This class enables: 1. A derived equivalence-invariant filtration S_\bullet(D⁽¹⁾(\mathscrX)) preserved under Fourier-Mukai transforms, 2. A birational invariant filtration S^SYZ_\bullet CH₀ on Bridgeland moduli spaces. We prove S^SYZ_\bullet CH₀ coincides with Voisin's filtration S^BV_\bulletCH₀ (Theorem 1.4), providing a canonical candidate for the conjectural Beauville-Voisin filtration. Applications include Bloch's conjecture for (anti)-symplectic automorphisms and existence of algebraically coisotropic subvarieties.

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