Makonzi, B. (2023) The Artin component and simultaneous resolution via reconstruction algebras of type A. Journal of Noncommutative Geometry, (doi: 10.4171/jncg/552) (Early Online Publication)
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Abstract
This paper uses noncommutative resolutions of non-Gorenstein singularities to construct classical deformation spaces by recovering the Artin component of the deformation space of a cyclic surface singularity using only the quiver of the corresponding reconstruction algebra. The relations of the reconstruction algebra are then deformed, and the deformed relations together with variation of the GIT quotient achieve the simultaneous resolution. This extends the work of Brieskorn, Kronheimer, Grothendieck, Cassens–Slodowy, and Crawley-Boevey–Holland into the setting of singularities C 2 /H with H≤GL(2,C) and furthermore gives a prediction for what is true more generally.
| Item Type: | Articles |
|---|---|
| Status: | Early Online Publication |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | MAKONZI, BRIAN |
| Authors: | Makonzi, B. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | Journal of Noncommutative Geometry |
| Publisher: | European Mathematical Society |
| ISSN: | 1661-6952 |
| ISSN (Online): | 1661-6960 |
| Published Online: | 05 December 2023 |
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