Home /  Workshop /  Schedules /  Positivity of the Chow-Mumford line bundle for families of K-stable Q-Fano varieties

Positivity of the Chow-Mumford line bundle for families of K-stable Q-Fano varieties

Recent Progress in Moduli Theory May 06, 2019 - May 10, 2019

May 07, 2019 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Zsolt Patakfalvi (École Polytechnique Fédérale de Lausanne (EPFL))
Location: SLMath: Eisenbud Auditorium
Video

6-Patakfalvi

Abstract

The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of polarized varieties, in particular on the base of families of Q-Fano varieties (that is, Fano varieties with klt singularities). It is conjectured that the CM line bundle yields a polarization on the conjectured moduli space of K-polystable Q-Fano varieties. This boils down to showing semi-positivity and positivity statements about the CM-line bundle for families with K-semi-stable and K-polystable Q-Fano fibers, respectively. I present a joint work with Giulio Codogni where we prove the necessary semi-positivity statements in the K-semi-stable situation, and the necessary positivity statements in the uniform K-stable situation, including in both cases variants assuming K-stability only for very general fibers. Our statements work in the most general singular situation (klt singularities), and the proofs are algebraic, except the computation of the limit of a sequence of real numbers via the central limit theorem of probability theory. I also present applications to fibered Fano varieties.

Supplements
Asset no preview Notes 1.69 MB application/pdf Download
Video/Audio Files

6-Patakfalvi

H.264 Video 869_26597_7729_6-Patakfalvi.mp4
Troubles with video?

Please report video problems to itsupport@slmath.org.

See more of our Streaming videos on our main VMath Videos page.