Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

20^th  of February 2024, 14:30-16:00, room “Dal Passo”

 

 

 

 

 

 

 

CM-minimizers and standard models of Fano fibrations over curves

 

 

Maksym Fedorchuk
Boston College

 

 

A recent achievement in K-stability of Fano varieties is an
algebro-geometric construction of a projective moduli space of
K-polystable Fanos. The ample line bundle on this moduli space is the
CM line bundle of Tian. One of the consequences of the general theory
is that given a family of K-stable Fanos over a punctured curve, the
polystable filling is the one that minimizes the degree of the CM line
bundle after every finite base change. A natural question is to
ask what are the CM-minimizers without base change. In
answering this question, we arrive at a theory of Kollár stability
for fibrations over one-dimensional bases, and standard models of Fano
fibrations. After explaining the general theory, I will sketch work in
progress on standard models of quartic threefold hypersurfaces. This
talk is based on joint work with Hamid Abban and Igor Krylov.

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry