Mori dream spaces and birational rigidity of Fano 3-folds
  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. 
Hamid Abban and Francesco Zucconi
math.AG