Erik Paemurru (Sofia): Local inequalities for cA_k singularities

Classically, birational rigidity proofs have involved a tower of blowups at smooth centers. On the other hand, the classification of three-dimensional divisorial contractions is best described in terms of weighted blowups. In a joint work with Igor Krylov and Takuzo Okada, we generalize an intersection-theoretic local inequality of Fulton–Lazarsfeld to weighted blowups. Using this together with the Noether–Fano inequality and the classification of 3-dimensional divisorial contractions, we prove nonrationality of many families of terminal Fano 3-folds.