On varieties with Ulrich twisted conormal bundles

Vincenzo Antonelli; Gianfranco Casnati; Angelo Felice Lopez; Debaditya Raychaudhury

On varieties with Ulrich twisted conormal bundles

Algebraic Geometry 2024-06-11 v2

Authors: Vincenzo Antonelli , Gianfranco Casnati , Angelo Felice Lopez , Debaditya Raychaudhury

Abstract

We study varieties $X \subset P^r$ such that is $N_X^*(k)$ is an Ulrich vector bundle for some integer $k$ . We first prove that such an $X$ must be a curve. Then we give several examples of curves with $N_X^*(k)$ an Ulrich vector bundle.

Keywords

Ulrich vector bundle conormal bundle projective variety curve algebraic geometry

Cite

@article{arxiv.2306.00113,
  title  = {On varieties with Ulrich twisted conormal bundles},
  author = {Vincenzo Antonelli and Gianfranco Casnati and Angelo Felice Lopez and Debaditya Raychaudhury},
  journal= {arXiv preprint arXiv:2306.00113},
  year   = {2024}
}

Comments

v2: we specified the results that hold in characteristic zero and the ones holding in any characteristic. Thanks to crucial remarks of anonymous referee, we improved Theorem 3(ii) to $g \ge 3$ and we rewrote completely and shortened section 8 by using interpolation techniques

On varieties with Ulrich twisted conormal bundles

Abstract

Keywords

Cite

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