Lefschetz decompositions and categorical resolutions of singularities

• Alexander Kuznetsov ^[1]
  1. [1] Steklov Mathematical Institute

     Steklov Mathematical Institute

     Rusia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 4, 2008, págs. 661-696
• Idioma: inglés
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• Resumen

  • Let Y be a singular algebraic variety and let Ye be a resolution of singularities of Y . Assume that the exceptional locus of Ye over Y is an irreducible divisor Ze in Ye. For every Lefschetz decomposition of the bounded derived category D b (Ze) of coherent sheaves on Ze we construct a triangulated subcategory D ⊂ D e b (Ye) which gives a desingularization of D b (Y ). If the Lefschetz decomposition is generated by a vector bundle tilting over Y then De is a noncommutative resolution, and if the Lefschetz decomposition is rectangular, then De is a crepant resolution