Algebraic Geometry Seminar: "Gale duality and the linearisation map for quiver moduli"

Abstract: I'll talk about the linearisation map for fine quiver moduli spaces. These spaces are constructed as geometric invariant theory quotients X//G, and the linearisation map assigns to each character of G the corresponding line bundle on the quotient X//G obtained by descent.  I'll present natural geometric conditions that guarantee this map to the Picard group is surjective and I'll describe the geometry that is encoded in the Gale dual map. The key point of the talk is to examine two matrices - one for the linearisation map and the other for its Gale dual - and to show that two rival interpretations of `Reid's recipe' for a finite subgroup of SL(3,C) actually encode the same information. 

Host: Ben Wormleighton