Derived equivalence for the simple flop of type D₄ via tilting bundles

2025/08/06 by Hara, Wahei
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.04579

Abstract

The aim of this article is to discuss the derived equivalence problem for a local model of the simple flop of type D₄, which was found by Kanemitsu. First, tilting bundles on both sides of the flop are constructed, and then those tilting bundles are applied to prove the derived equivalence. This derived equivalence for the flop deduces derived equivalences between general K3 surfaces of degree 12. The study of this example of a flop is very similar to the author's previous work for the simple of flop of type G₂^†, but the construction and the analysis of tilting bundles become harder.

Citations

• Derived equivalence for the simple flop of type D₅
• Mutations of noncommutative crepant resolutions in geometric invariant theory
• Non-commutative crepant resolutions, an overview
• Mukai pairs and simple K-equivalence
• Deformation of tilting-type derived equivalences for crepant resolutions
• On derived equivalence for Abuaf flop: mutation of non-commutative crepant resolutions and spherical twists
• Derived equivalence and Grothendieck ring of varieties: the case of K3 surfaces of degree 12 and abelian varieties
• Equivalence of the Derived Category of a Variety with a Singularity\n Category
• Tilting generators via ample line bundles
• Flops connect minimal models
• Derived categories of coherent sheaves
• Non-commutative crepant resolutions
• D-equivalence and K-equivalence
• Mukai flops and derived categories

Related

• Derived equivalence for the simple flop of type G₂^† via tilting bundles
• Derived equivalences for the flops of type C₂ and A^G₄ via mutation of semiorthogonal decomposition
• Deformation of tilting-type derived equivalences for crepant resolutions
• Derived equivalence for the simple flop of type D₅
• Derived Equivalences of Generalized Grassmannian Flops: D₄ and G₂^† Cases