Fano varieties with extreme behavior

Abstract: It is attractive to classify Fano varieties with various types of singularities that originated from the minimal model program. For a Fano variety, the Fano index is the largest integer $m$ such that the anti-canonical divisor is $\mathbb{Q}$-linearly equivalent to m times some Weil divisor. For Fano varieties of various singularities, I show the Fano indexes can grow double exponentially with respect to the dimension. Those examples are also conjecturally optimal and have a close connection with Calabi-Yau varieties of extreme behavior.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html