We compute a class of Sarkisov links from Fano 3-folds embedded in weighted Grassmannians using explicit methods for describing graded rings associated to a variation of geometric invariant theory (GIT) quotient.
"Graded rings of rank 2 Sarkisov links." Nagoya Math. J. 197 1 - 44, March 2010. https://doi.org/10.1215/00277630-2009-001