Back to Algebraic Geometry Seminar: Fall 2021
Algebraic Geometry Seminar
Date: Tuesday, Sep 28, 2021
Time: 3:30PM - 4:30PM
Location: Zoom
LCB 121
Devlin Mallory
University of Utah
Title |
Bigness of tangent bundles, differential operators, and reduction mod \(p\) (In-person talk) |
Abstract |
Since Bernstein—Gelfand—Gelfand’s analysis of the ring of differential operators on the cone over an elliptic curve, geometric reasoning has provided one of the few known methods for the difficult algebraic problem of describing the differential operators on a singular ring in characteristic 0. Attempts to study similar phenomena in higher dimension lead naturally to the study of positivity (bigness) of the tangent bundle of Fano varieties, a question which is of independent interest and which parallels well-known theorems and conjectures regarding the ampleness and nefness of the tangent bundle. In this talk, we will review recent progress on this problem, and (more significantly) the questions that remain unknown. We’ll also point out the consequence this study has for several phenomena regarding reduction to positive characteristic, including questions about associated primes of local cohomology modules in mixed characteristic and the question of reduction of log canonical singularities mod (p). |
Algebraic Geometry