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Lieven LeBruyn and Stijn Symens. Partial desingularizations arising from non-commutative algebras. arXiv/math.RA, 0507494:, 2005. math.RA/0507494
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.
@article{LeBruyn2005a,
author={LeBruyn, Lieven and Stijn Symens},
title={Partial desingularizations arising from non-commutative algebras},
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.},
journal={arXiv/math.RA},
volume={0507494},
year={2005},
bib2html_pubtype ={Papers},
bib2html_rescat ={Noncommutative Geometry},
bib2html_dl_html={http://arxiv.org/abs/math.RA/0507494},
pages={},
language={English},
note={math.RA/0507494}
}
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