$\ell$-away ACM line bundles on a nonsingular cubic surface

Debojyoti Bhattacharya; A. J. Parameswaran; Jagadish Pine

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arXiv · 2408.04464

$\ell$-away ACM line bundles on a nonsingular cubic surface

Debojyoti Bhattacharya·A. J. Parameswaran·Jagadish Pine

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Abstract

Let $X \subset \mathbb P^3$ be a nonsingular cubic hypersurface. Faenzi (\cite{F}) and later Pons-Llopis and Tonini (\cite{PLT}) have completely characterized ACM line bundles over $X$. As a natural continuation of their study in the non-ACM direction, in this paper, we completely classify $\ell$-away ACM line bundles (introduced recently by Gawron and Genc (\cite{GG})) over $X$, when $\ell \leq 2$. For $\ell\geq 3$, we give examples of $\ell$-away ACM line bundles on $X$ and for each $\ell \geq 1$, we establish the existence of smooth hypersurfaces $X^{(d)}$ of degree $d >\ell$ in $\mathbb P^3$ admitting $\ell$-away ACM line bundles.

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BibTeX RIS

Debojyoti Bhattacharya, A. J. Parameswaran, Jagadish Pine. 2024-08-08. $\ell$-away ACM line bundles on a nonsingular cubic surface. https://arxiv.org/abs/2408.04464

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