Algebraic Geometry Seminar

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Classification and Birational Rigidity of Del Pezzo Fibrations with an Action of the Klein Simple Group

Speaker: Igor Krylov, University of Edinburgh

Location: Warren Weaver Hall 201

Date: Thursday, March 10, 2016, 3:30 p.m.

Synopsis:

Let G be a finite subgroup of the Cremona group. The study of embeddings of G into the Cremona group is equivalent to the study of the G-birational geometry of rational G-Mori fiber spaces. This approach works particularly well for simple subgroups. I prove that any del Pezzo fibration over the projective line with an action of the Klein simple group is either P² x P¹ or a certain del Pezzo fibration X_n of degree 2. The variety X_n has 2n quotient singularities of the type 1/2(1,1,1). I prove that the varieties X_n are rigid, in particular not rational, for n>2.