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arXiv · 1209.1564

Wonderful resolutions and categorical crepant resolutions of singularities

Roland Abuaf
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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. We also discuss notions of minimality for a categorical resolution of singularities and we explore some links between minimality and crepancy for such resolutions.

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Roland Abuaf. 2013-09-03. Wonderful resolutions and categorical crepant resolutions of singularities. https://arxiv.org/abs/1209.1564

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