Resumen de Lefschetz decompositions and categorical resolutions of singularities

Alexander Kuznetsov

• 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