Wonderful resolutions and categorical crepant resolutions of singularities

Abstract

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.