Mori dream spaces and birational rigidity of Fano 3-folds

Abstract

We highlight a relation between the existence of Sarkisov links and the finite generation of (certain) Cox rings. We introduce explicit methods to use this relation in order to prove birational rigidity statements. To illustrate, we complete the birational rigidity results of Okada for Fano complete intersection 3-folds in singular weighted projective spaces.

arXiv commentSmall modifications, including a change in the title. Final version to appear in Advances in Mathematics