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Images of toric varieties and liftability of the Frobenius morphism

Banff International Research Station for Mathematical Innovation and Discovery

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 varieties such as abelian varieties (Demailly-Hwang-Mok-Peternell) or toric varieties (Occhetta-Wiśniewski). 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 Jakub Witaszek and Maciej Zdanowicz.

Mathematics; Algebraic geometry; Convex and discrete geometry

video/mp4

Author affiliation: IHES

2017-11-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63565

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/