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The Geometry of Noncommutative Singularity Resolutions
- Publication Year :
- 2011
-
Abstract
- We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this conjecture for all cyclic quotient surface singularities, the Kleinian D_n and E_6 surface singularities, the conifold singularity, and a non-isolated singularity, using appropriate quiver algebras. This conjecture provides a possible new generalization of the classical McKay correspondence. Then, using symplectic reduction within these rings, we obtain new, non-conventional resolutions that are hidden if only commutative functions are considered. Geometrically, these non-conventional resolutions result from shrinking exceptional loci to ramified (non-Azumaya) point-like spheres.<br />Comment: 42 pages. Comments welcome
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1102.5741
- Document Type :
- Working Paper