On projective varieties with strictly nef tangent bundles

Abstract

In this paper, we study smooth complex projective varieties $X$ such that some exterior power ${\bigwedge }^r{T}_X$ of the tangent bundle is strictly nef. We prove that such varieties are rationally connected. We also classify the following two cases. If $T_X$ is strictly nef, then $X$ isomorphic to the projective space ${\mathrm{P}}^n$. If ${\bigwedge }^2{T}_X$ is strictly nef and if $X$ has dimension at least $3$, then $X$ is either isomorphic to ${\mathrm{P}}^n$ or a quadric ${\mathrm{Q}}^n$.

This article supersedes arXiv:1609.06867. To appear in J. Math. Pures Appl

References in corpus (1)

• Cohomological characterizations of projective spaces and hyperquadrics