Lefschetz decompositions and Categorical resolutions of singularities

Original · EN

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