Back to Algebraic Geometry Seminar: Spring 2012
Algebraic Geometry Seminar
Date: Tuesday, Jan 17, 2012
Time: 3:30PM - 4:30PM
Location: LCB 222
Noah Giansiracusa
Universität Zürich
Title |
GIT compactifications of \(M_{0,n}\) and flips |
Abstract |
Despite intensive investigation over the years and its innocuously classical appearance, there remain some tantalizing open questions regarding the birational geometry of the moduli space of marked rational curves. One such question, dating from a 2000 paper of Hu and Keel, is to determine whether (\bar{M}{0,n}) is a Mori dream space. Roughly speaking, this would say that its Mori-theoretic information is completely determined by variational GIT in a natural way. In this talk I will discuss joint work with Dave Jensen and Han-Bom Moon in which we construct a wide range of birational models using a GIT construction inspired by two constructions of Kapranov from 1993. These models include (\bar{M}{0,n}) itself as well as all the Hassett weighted models. A consequence is that we exhibit explicit flips between models and give a glimpse of the Mori dream behavior envision by Hu and Keel. |
Algebraic Geometry