Positivity of the exterior power of the tangent bundles

Abstract: By Mori's solution of the Hartshorne conjecture, the only smooth projective variety with ample tangent bundle is the projective space. As a generalization of the Hartshorne conjecture, Demially, Peternell and Schneider studied smooth projective varieties with nef tangent bundle. They proved that such variety X admits an étale cover Y such that the Albanese map Y \to Alb(Y) is a smooth morphism whose fibers are smooth Fano varieties with nef tangent bundle. In this talk, we will study smooth projective varieties such that the r-th exterior power of the tangent bundle is nef, paying special attention to the case r=2. This talk is based on the paper arXiv:2011.01427.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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