Mathematics – Algebraic Geometry
Scientific paper
2011-02-28
Mathematics
Algebraic Geometry
42 pages. Comments welcome
Scientific paper
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.
Beil Charlie
No associations
LandOfFree
The Geometry of Noncommutative Singularity Resolutions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Geometry of Noncommutative Singularity Resolutions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Geometry of Noncommutative Singularity Resolutions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-426244