Algebraic Geometry Seminar | Fano fourfolds with large anticanonical base locus

Fano fourfolds with large anticanonical base locus

A famous theorem of Shokurov states that a general anticanonical divisor of a smooth Fano threefold is a smooth K3 surface. This is quite surprising since there are several examples where the base locus of the anticanonical system has codimension two. In this paper we show that for four-dimensional Fano manifolds the behaviour is completely opposite: if the base locus is a normal surface, hence has codimension two, all the anticanonical divisors are singular. This is joint work with Saverio Secci.

About the speaker

Andreas Höring｜Université Côte d'Azur

Andreas Höring is a distinguished researcher in complex algebraic geometry. He specializes in understanding the solution sets of polynomial equations in several variables through the use of algebraic, analytical, and geometrical tools.

His research primarily focuses on classifying complex projective varieties and compact Kählerian varieties of dimension at least three.

His unique approach involves utilizing holomorphic foliations to enrich Mori's theory (minimal models program).