Back to Algebraic Geometry Seminar: Fall 2024
Algebraic Geometry Seminar
Date: Tuesday, Aug 27, 2024
Time: 3:30PM - 4:30PM
Location: LCB 222
Suchitra Pande
University of Utah
Title |
Positivity of the Limit F-signature |
Abstract |
The F-signature of a local singularity is an invariant in positive characteristics that measures the asymptotic properties of the Frobenius map. It can be used to detect regularity, strong F-regularity and other finiteness properties in positive characteristics. Thus, the F-signature seems to play a role analogous to the local volume of KLT singularities over the complex numbers. This talk concerns the behavior of the F-signature under the process of reduction to characteristic p » 0 of a fixed complex singularity. Motivated by applications to the sizes of local fundamental groups, Carvajal-Rojas, Schwede and Tucker conjectured that the F-signatures remain uniformly bounded away from zero when we reduce a complex KLT singularity to large characteristics . We will present joint works with Yuchen Liu, and with Anna Brosowsky, Izzet Coskun and Kevin Tucker, in which we prove this conjecture in many new cases including for cones over low degree smooth hypersurfaces and most three dimensional KLT singularities. We will present some of the key ideas in the proof, which come from the K-stability theory of Fano varieties. |
Algebraic Geometry