Abstract Marcel Maslovaric
GIT and Mori dream spaces
Abstract: When forming a quotient via Geometric Invariant Theory (GIT) we need to specify a notion of stability. Different choices of stability give different quotients, which are related by rational maps.
In this talk I want to explain how the space of stability notions is related to the birational geometry of the quotients. This will incorporate the space of line bundles on the quotients and the various cones therein (nef, effective, moving).
More concretely, I will focus on the case of a Mori dream space, where this interplay works very well.