Back to Algebraic Geometry Seminar: Spring 2017
Algebraic Geometry Seminar
Date: Tuesday, Mar 7, 2017
Time: 3:30PM - 4:30PM
Location: LCB 219
Jakub Witaszek
Imperial College London
Title |
Images of toric varieties and liftability of the Frobenius morphism |
Abstract |
The celebrated proof of the Hartshorne conjecture by Shigefumi Mori allowed for the study of the geometry of higher dimensional varieties through the analysis of deformations of rational curves. One of the many applications of Mori’s results was Lazarsfeld’s positive answer to the conjecture of Remmert and Van de Ven which states that the only smooth variety that the projective space can map surjectively onto, is the projective space itself. Motivated by this result, a similar problem has been considered for other kinds of manifolds such as abelian varieties (Demailly-Hwang-Mok-Peternell) or toric varieties (Occhetta-Wi?niewski). In my talk, I would like to present a completely new perspective on the problem coming from the study of Frobenius lifts in positive characteristic. This is based on a joint project with Piotr Achinger and Maciej Zdanowicz. |
Algebraic Geometry