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Partial Desingularizations Arising from Non-Commutative Algebras

Lieven Le Bruyn·Stijn Symens
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Abstract

Let X be a singular affine normal variety with coordinate ring R and assume that there is an R-order admitting a stability structure such that the scheme of relevant semistable representations is smooth, then we construct a partial desingularization of X with classifiable remaining singularities. In dimension 3 this explains the omnipresence of conifold singularities in partial desingularizations of quotient singularities. In higher dimensions we have a small list of singularity types generalizing the role of the conifold singularity.

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Lieven Le Bruyn, Stijn Symens. 2005-07-23. Partial Desingularizations Arising from Non-Commutative Algebras. https://arxiv.org/abs/math/0507494

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