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The Artin component and simultaneous resolution via reconstruction algebras of type A.
- Source :
- Journal of Noncommutative Geometry; 2024, Vol. 18 Issue 4, p1229-1264, 36p
- Publication Year :
- 2024
-
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 C²/H with H ≤ GL(2, C) and furthermore gives a prediction for what is true more generally. [ABSTRACT FROM AUTHOR]
- Subjects :
- RELATION algebras
ALGEBRA
FORECASTING
NONCOMMUTATIVE algebras
Subjects
Details
- Language :
- English
- ISSN :
- 16616952
- Volume :
- 18
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Journal of Noncommutative Geometry
- Publication Type :
- Academic Journal
- Accession number :
- 179545922
- Full Text :
- https://doi.org/10.4171/JNCG/552