Algebraic Geometry Seminar
Anne-Sophie Kaloghiros
Cambridge/UIC
The Sarkisov Program
Abstract: The goal of the Minimal Model Program is to produce "good" representatives
of birational equivalence classes of varieties. If X is a smooth projective
variety, the MMP (conjecturally) produces in a finite number of elementary
steps either a minimal model, or, if X is uniruled, a Mori fibre space.
However, this good representative is not unique. It is natural to ask when
two minimal models or when two Mori fibre spaces are birational.
In the case of Mori fibre spaces, Hacon and McKernan recently proved that
any birational map between Mori fibre spaces may be decomposed into a finite
number of "elementary Sarkisov links". This decomposition is not unique.
Their proof is based on recent advances in Mori Theory. I will present their
argument, and show how to understand/describe relations in the Sarkisov
program. If time permits, I will show more definite applications of this
approach to the case of 3-folds.
Note special day (Monday).
Monday October 10, 2011 at 4:00 PM in SEO 427