Positivity of the exterior power of the tangent bundles

2022/08/13 by Watanabe, Kiwamu
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.06735

Abstract

Let X be a complex smooth projective variety such that the exterior power of the tangent bundle \bigwedge^r T_X is nef for some 1≤ r<dim X. We prove that, up to an étale cover, X is a Fano fiber space over an Abelian variety. This gives generalizations of the structure theorem of varieties with nef tangent bundle by Demailly, Peternell and Schneider and that of varieties with nef \bigwedge² T_X by the author. Our result also gives an answer to a question raised by Li, Ou and Yang for varieties with strictly nef \bigwedge^r T_X when r < dim X.

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