Algebraic Geometry and Combinatorics Seminar: Local inequalities for $cA_k$ singularities

Abstract: Proofs in birational geometry have traditionally involved a composition of blowups at smooth centres. At the same time, the most natural description of divisorial contractions in dimension 3 uses weighted blowups. In this talk, I will discuss a generalization of an intersection-theoretic local inequality of Fulton–Lazarsfeld to weighted blowups. As an application, we prove nonrationality of many families of terminal Fano 3-folds. This is a joint work with Igor Krylov and Takuzo Okada.

Host: Matt Kerr