Wonderful resolutions and categorical crepant resolutions of singularities
-
Roland Abuaf
Abstract
Let X be an algebraic variety with Gorenstein singularities. We define the notion of a wonderful resolution of singularities of X by analogy with the theory of wonderful compactifications of semi-simple linear algebraic groups. We prove that if X has rational singularities and has a wonderful resolution of singularities, then X admits a categorical crepant resolution of singularities. As an immediate corollary, we get that all determinantal varieties defined by the minors of a generic square/symmetric/skew-symmetric matrix admit categorical crepant resolution of singularities.
I would like to thank Sasha Kuznetsov for many interesting discussions on categorical resolutions of singularities and Christian Lehn for many helpful comments on the first drafts of this paper. I would also like to thank Laurent Manivel for his constant support and insightful criticism during the preparation of this work.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem
- A Giambelli formula for even orthogonal Grassmannians
- Lifting in Frattini covers and a characterization of finite solvable groups
- Note on basic features of large time behaviour of heat kernels
- A decomposition theorem in II1-factors
- Wonderful resolutions and categorical crepant resolutions of singularities
- Tannaka–Kreĭn duality for compact quantum homogeneous spaces II. Classification of quantum homogeneous spaces for quantum SU(2)
- An approach of the minimal model program for horospherical varieties via moment polytopes
- Height of exceptional collections and Hochschild cohomology of quasiphantom categories
Articles in the same Issue
- Frontmatter
- The length metric on the set of orthogonal projections and new estimates in the subspace perturbation problem
- A Giambelli formula for even orthogonal Grassmannians
- Lifting in Frattini covers and a characterization of finite solvable groups
- Note on basic features of large time behaviour of heat kernels
- A decomposition theorem in II1-factors
- Wonderful resolutions and categorical crepant resolutions of singularities
- Tannaka–Kreĭn duality for compact quantum homogeneous spaces II. Classification of quantum homogeneous spaces for quantum SU(2)
- An approach of the minimal model program for horospherical varieties via moment polytopes
- Height of exceptional collections and Hochschild cohomology of quasiphantom categories
