Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

5^th of December 2023, 14:30-16:00, room “D’Antoni”

 

 

 

 

 

 

 

 

Stability conditions for varieties

 

 

Ruadhaí Dervan

University of Glasgow

 

Stability conditions in algebraic geometry are used to construct moduli spaces. Experience from the theory of vector bundles (and coherent sheaves) suggests it is useful to have many stability conditions, so that one can geometrically understand the birational behaviour of resulting moduli spaces by varying the stability condition. Motivated by this, I will describe a mostly conjectural analogous story for projective varieties with an ample line bundle. Here the classical notion of stability is K-stability, which aims to construct higher dimensional analogues of the moduli space of stable curves, and the main point will be to introduce variants of K-stability defined using extra topological choices. The main results will link these new stability conditions with differential geometry, through the solvability of certain geometric PDEs, and I will try to explain how these links come about and what the general picture should be.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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