Lefschetz decompositions and Categorical resolutions of singularities

2006/09/08 by Alexander Kuznetsov, Kuznetsov, Alexander · 4 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0609240

openalex publication_date 2006/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Y be a singular algebraic variety and let \TY be a resolution of singularities of Y. Assume that the exceptional locus of \TY over Y is an irreducible divisor \TZ in \TY. For every Lefschetz decomposition of \TZ we construct a triangulated subcategory \TD ⊂ \D^b(\TY) which gives a desingularization of \D^b(Y). If the Lefschetz decomposition is generated by a vector bundle tilting over Y then \TD is a noncommutative resolution, and if the Lefschetz decomposition is rectangular, then \TD is a crepant resolution.

Citations

• McKay equivalence for symplectic resolutions of singularities

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