Effective non-vanishing for weighted complete intersections of low codimension
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916579272294400 |
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| author | Passantino, Alessandro |
| author_facet | Passantino, Alessandro |
| contents | We show that on quasi-smooth weighted complete intersections of codimension at most 3, any ample Cartier divisor $H$ such that $H-K_X$ is ample admits a nontrivial global section. This is done by proving a generalisation of a numerical conjecture formulated by Pizzato, Sano and Tasin, which relates the existence of global sections of $H$ to the Frobenius number of the numerical semigroup generated by the weights of the ambient projective space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective non-vanishing for weighted complete intersections of low codimension Passantino, Alessandro Algebraic Geometry Number Theory 14J40 (Primary), 20M14 (Secondary) We show that on quasi-smooth weighted complete intersections of codimension at most 3, any ample Cartier divisor $H$ such that $H-K_X$ is ample admits a nontrivial global section. This is done by proving a generalisation of a numerical conjecture formulated by Pizzato, Sano and Tasin, which relates the existence of global sections of $H$ to the Frobenius number of the numerical semigroup generated by the weights of the ambient projective space. |
| title | Effective non-vanishing for weighted complete intersections of low codimension |
| topic | Algebraic Geometry Number Theory 14J40 (Primary), 20M14 (Secondary) |
| url | https://arxiv.org/abs/2501.13267 |