Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: McKay correspondence and walls for G-Hilb

Seminar | October 29 | 5-6 p.m. | 939 Evans Hall

 Ben Wormleighton, UC Berkeley

 Department of Mathematics

The McKay correspondence studies how the representation theory of subgroups G of SL(n) interacts with the geometry of minimal resolutions of the quotient singularity \(\mathbb C^n / G\). I will outline the classical story for SL(2) and some of its extensions to three dimensions through quivers, CM-modules, and derived categories. One of the outcomes of this is that all minimal resolutions (at least when G is abelian) correspond to chambers in a stability space, though the chamber structure is in general quite difficult to study. I will describe my recent work (some joint with Yukari Ito) that produces equations for the walls of the chamber for a special resolution directly from its geometry and the corresponding representation theory, and that also clarifies the wall-crossing behaviour at each wall.