Notes on symplectic action on (2,1)-cycles on K3 surfaces

2025/09/16 by Ken Sato, Sato, Ken
Mathematics · #14C25 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2509.13491

openalex publication_date 2025/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose and study a conjecture that symplectic automorphisms of a K3 surface X act trivially on the indecomposable part CH²(X,1)_ind⊗ ℚ of Bloch's higher Chow group. This is a higher Chow analogue of Huybrechts' conjecture on the symplectic action on 0-cycles. We give several partial results verifying our conjecture, some conditional and some unconditional. Our unconditional results include the full proof for Kummer surfaces of product type.

Citations

• Higher Chow cycles on Eisenstein K3 surfaces
• Beilinson's Hodge conjecture for smooth varieties
• Some remarks on Brauer groups of K3 surfaces

Related

• Higher Chow cycles on Eisenstein K3 surfaces
• Higher Chow cycles on K3 surfaces attached to plane quartics
• Higher Chow Cycles on an Abelian Surface and a non-Archimedean analogue of the Hodge-D-conjecture
• Real Regulators on Self-Products of K3 Surfaces
• On K₁ and K₂ of algebraic surfaces