Lower bounds for Seshadri constants on blow ups of $\mathbb{P}^2$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914032737320960 |
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| author | Jacob, Cyril J. |
| author_facet | Jacob, Cyril J. |
| contents | Let $π: X_r \rightarrow \mathbb P^2$ be a blow up of $\mathbb P^2$ at $r$ distinct points $p_1,p_2,\dots, p_r$. We study lower bounds for Seshadri constants of ample line bundles on $X_r$. First, we consider the case when the points lie on a curve of degree $d\le 3$, and the case when $r\le 8$. We then assume that the points are very general and show that $\varepsilon(X_r)\geq \frac{1}{2}$ if the Strong SHGH conjecture is true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lower bounds for Seshadri constants on blow ups of $\mathbb{P}^2$ Jacob, Cyril J. Algebraic Geometry 14C20, 14E05, 14H50 Let $π: X_r \rightarrow \mathbb P^2$ be a blow up of $\mathbb P^2$ at $r$ distinct points $p_1,p_2,\dots, p_r$. We study lower bounds for Seshadri constants of ample line bundles on $X_r$. First, we consider the case when the points lie on a curve of degree $d\le 3$, and the case when $r\le 8$. We then assume that the points are very general and show that $\varepsilon(X_r)\geq \frac{1}{2}$ if the Strong SHGH conjecture is true. |
| title | Lower bounds for Seshadri constants on blow ups of $\mathbb{P}^2$ |
| topic | Algebraic Geometry 14C20, 14E05, 14H50 |
| url | https://arxiv.org/abs/2404.11906 |