Positivity on Blow-up of hyperelliptic surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915217673289728 |
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| author | Roy, Praveen Kumar |
| author_facet | Roy, Praveen Kumar |
| contents | Let $X_r$ denote the blow-up of the hyperelliptic surface $X$ at $r$ very general points. In this paper, we first provide a criterion for the ampleness of a line bundle on $X_r$ and compare it with an existing result. We then study the multi-point Seshadri constants of ample line bundles on hyperelliptic surfaces $X$. Next, we compute single-point Seshadri constants on $X_r$ for specific ample line bundles on odd types. Furthermore, we show that the global Seshadri constants for certain ample line bundles on blow-up of hyperelliptic surfaces are rational. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positivity on Blow-up of hyperelliptic surfaces Roy, Praveen Kumar Algebraic Geometry 14C20 Let $X_r$ denote the blow-up of the hyperelliptic surface $X$ at $r$ very general points. In this paper, we first provide a criterion for the ampleness of a line bundle on $X_r$ and compare it with an existing result. We then study the multi-point Seshadri constants of ample line bundles on hyperelliptic surfaces $X$. Next, we compute single-point Seshadri constants on $X_r$ for specific ample line bundles on odd types. Furthermore, we show that the global Seshadri constants for certain ample line bundles on blow-up of hyperelliptic surfaces are rational. |
| title | Positivity on Blow-up of hyperelliptic surfaces |
| topic | Algebraic Geometry 14C20 |
| url | https://arxiv.org/abs/2503.22207 |