A twisted derived category of hyper-Kähler varieties of K3^[n]-type

2025/02/04 by Ruxuan Zhang, Zhang, Ruxuan
Mathematics · Physics and Astronomy · #14D20 #14F08 #14JJ42 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2502.02143

openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We conjecture that a natural twisted derived category of any hyper-Kähler variety of K3^[n]-type is controlled by its Markman-Mukai lattice. We prove the conjecture under numerical constraints, and our proof relies heavily on Markman's projectively hyperholomorphic bundle and a recently proven twisted version of the D-equivalence conjecture. In particular, we prove that any two fine moduli spaces of stable sheaves on a K3 surface are derived equivalent if they have the same dimension.

Related

• The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles
• Non-Fine Moduli Spaces of Sheaves on K3 Surfaces
• On Hyperkähler manifolds of K3^[n]-type with large Picard number
• Derived categories of hyper-Kähler manifolds: extended Mukai vector and integral structure
• Derived categories of generalized Kummer varieties: extended Mukai vector