Projective manifolds whose tangent bundle is Ulrich

Benedetti, Vladimiro; Montero, Pedro; Montañez, Yulieth Prieto; Troncoso, Sergio

doi:10.1016/j.jalgebra.2023.03.046

Journal of Algebra

2023

DOI: 10.1016/j.jalgebra.2023.03.046

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Projective manifolds whose tangent bundle is Ulrich

Vladimiro Benedetti

Pedro Montero

Yulieth Prieto Montañez

et al.

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Cited by 3 publications

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On varieties with Ulrich twisted tangent bundles

Lopez,

Raychaudhury

2023

Annali di Matematica

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We study varieties $$X \subseteq {\mathbb {P}}^N$$ X ⊆ P N of dimension n such that $$T_X(k)$$ T X ( k ) is an Ulrich vector bundle for some $$k \in {\mathbb {Z}}$$ k ∈ Z . First we give a sharp bound for k in the case of curves. Then we show that $$k \le n+1$$ k ≤ n + 1 if $$2 \le n \le 12$$ 2 ≤ n ≤ 12 . We classify the pairs $$(X,{\mathcal {O}}_X(1))$$ ( X , O X ( 1 ) ) for $$k=1$$ k = 1 and we show that, for $$n \ge 4$$ n ≥ 4 , the case$$k=2$$ k = 2 does not occur.

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On varieties with Ulrich twisted tangent bundles

Lopez,

Raychaudhury

2023

Annali di Matematica

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Tangent, cotangent, normal and conormal bundles are almost never instanton bundles

Casnati

2023

Communications in Algebra

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On varieties with Ulrich twisted conormal bundles

Antonelli,

Casnati,

Lopez

et al. 2024

Proc. Amer. Math. Soc.

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

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Projective manifolds whose tangent bundle is Ulrich

Cited by 3 publications

References 54 publications

On varieties with Ulrich twisted tangent bundles

On varieties with Ulrich twisted tangent bundles

Tangent, cotangent, normal and conormal bundles are almost never instanton bundles

On varieties with Ulrich twisted conormal bundles

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