Flops and derived categories

2000/09/06 by Tom Bridgeland, Bridgeland, Tom · 7 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/0009053

21 pp

arxiv created 2000/09/06 · openalex publication_date 2000/09/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper contains some applications of Fourier-Mukai techniques to the birational geometry of threefolds. In particular, we prove that birational Calabi-Yau threefolds have equivalent derived categories. To do this we show how flops arise naturally as moduli spaces of perverse coherent sheaves.

Citations

• Mukai implies McKay: the McKay correspondence as an equivalence of derived categories

Cited by

• Yoga for Fourier--Mukai partnership
• A simpler kernel for stratified Mukai flops
• Window categories for a simple 9-fold flop of Grassmannian type
• Spherical and Semibrick Classifications
• Moduli of non-pure sheaves and contractions of Hilbert schemes
• Simple complexes on a flopped curve
• Derived autoequivalences of length 2 flops via GIT

Related

• Flops and Equivalences of derived Categories for Threefolds with only Gorenstein Singularities
• Categories derivees et geometrie birationnelle
• Flops and about: a guide
• Window categories for a simple 9-fold flop of Grassmannian type
• Flops, flips and perverse point sheaves on threefold stacks