$\ell$-away ACM line bundles on a nonsingular cubic surface
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| Format: | Preprint |
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2024
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| _version_ | 1866929453046693888 |
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| author | Bhattacharya, Debojyoti Parameswaran, A. J. Pine, Jagadish |
| author_facet | Bhattacharya, Debojyoti Parameswaran, A. J. Pine, Jagadish |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\ell$-away ACM line bundles on a nonsingular cubic surface Bhattacharya, Debojyoti Parameswaran, A. J. Pine, Jagadish Algebraic Geometry 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. |
| title | $\ell$-away ACM line bundles on a nonsingular cubic surface |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.04464 |