Varieties of general type with small volume

Abstract: By Hacon-McKernan, Takayama, and Tsuji, there is a constant r_n such that for every r at least r_n, the r-canonical map of every n-dimensional variety of general type is birational. In this talk, we show that r_n must grow faster than any polynomial in n, by giving examples of general type with small volume in high dimensions. In particular, we construct a klt n-fold with ample canonical class whose volume is less than 1/2^(2^n). The klt examples should be close to optimal. This is joint work with Burt Totaro.

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