Seminario di algebra e geometria
ore
14:15
presso Aula Arzelà
Finding minimal models is the first step in the birational
classification of smooth projective varieties. After it is established that a
minimal model exists some natural questions arise such as: is it the minimal
model unique? If not, how many are they? After recalling all the necessary
notions of the Minimal Model Program, I will explain that varieties of
general type admit a finite number of minimal models. I will talk about a
recent joint project with Stefan Schreieder and Luca Tasin where we prove
that this number is bounded by a constant depending only on the canonical volume.
It follows that in any dimension, minimal models of general type and bounded volume form a bounded family.
I will also show that in some cases for threefolds, it is possible
to compute this constant explicitly.