Varieties with Ulrich exterior powers of the tangent bundle

Yuta Takahashi; Kiwamu Watanabe

Varieties with Ulrich exterior powers of the tangent bundle

Algebraic Geometry 2026-06-26 v1 Commutative Algebra

Authors: Yuta Takahashi , Kiwamu Watanabe

Abstract

We study smooth polarized projective varieties $(X,H)$ whose exterior powers of the tangent bundle are Ulrich. We prove that if $\bigwedge^rT_X$ is $H$ -Ulrich for some $0<r<\dim X$ , then $X$ is Fano and the intersection number $(-K_X)\cdot H^{n-1}$ is determined explicitly. We then classify the Picard number one case: the only example is the Veronese surface $(\mathbb P^2,\mathcal O_{\mathbb P^2}(2))$ .

Keywords

Ulrich bundle Tangent bundle Exterior power Polarized projective variety Fano variety Picard number

Cite

@article{arxiv.2606.27851,
  title  = {Varieties with Ulrich exterior powers of the tangent bundle},
  author = {Yuta Takahashi and Kiwamu Watanabe},
  journal= {arXiv preprint arXiv:2606.27851},
  year   = {2026}
}

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19 pages