Explicit Effective Birationality for Singular Surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915462207504384 |
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| author | Bie, Pinxian |
| author_facet | Bie, Pinxian |
| contents | We give some explicit upper bounds on the effective birationality of the canonical or anti-canonical system for a singular surface. In particular, we show that for any surface $X$ with $ε$-lc singularity and the canonical divisor $K_X$ or the anti-canonical divisor $-K_X$ is big and nef, then there exists explicit natural numbers $m$ and $l$ depending only on $ε$ such that $|mK_X|$ or $|-lK_X|$ defines a birational map. Although these explicit values are expected to be far from optimal, they are the first explicit upper bounds of this type for surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit Effective Birationality for Singular Surfaces Bie, Pinxian Algebraic Geometry 14E30 (Primary) 14E05, 14J17 (Secondary) We give some explicit upper bounds on the effective birationality of the canonical or anti-canonical system for a singular surface. In particular, we show that for any surface $X$ with $ε$-lc singularity and the canonical divisor $K_X$ or the anti-canonical divisor $-K_X$ is big and nef, then there exists explicit natural numbers $m$ and $l$ depending only on $ε$ such that $|mK_X|$ or $|-lK_X|$ defines a birational map. Although these explicit values are expected to be far from optimal, they are the first explicit upper bounds of this type for surfaces. |
| title | Explicit Effective Birationality for Singular Surfaces |
| topic | Algebraic Geometry 14E30 (Primary) 14E05, 14J17 (Secondary) |
| url | https://arxiv.org/abs/2508.18237 |