Positivity of higher exterior powers of the tangent bundle

Cécile Gachet

Positivity of higher exterior powers of the tangent bundle

Algebraic Geometry 2024-12-13 v4

Authors: Cécile Gachet

Abstract

We prove that a smooth projective variety $X$ of dimension $n$ with strictly nef third, fourth or $(n-1)$ -th exterior power of the tangent bundle is a Fano variety. Moreover, in the first two cases, we provide a classification for $X$ under the assumption that $\rho(X)\ne 1$ .

Keywords

smooth projective variety tangent bundle exterior power strictly nef fano variety classification

Cite

@article{arxiv.2207.10854,
  title  = {Positivity of higher exterior powers of the tangent bundle},
  author = {Cécile Gachet},
  journal= {arXiv preprint arXiv:2207.10854},
  year   = {2024}
}

Comments

[v4]: final version, updated after referee report

Related papers

View all related →