Optimal upper bounds for anti-canonical volumes of singular toric Fano varieties
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910711865671680 |
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| author | Zou, Yu |
| author_facet | Zou, Yu |
| contents | Fix two positive integers $d\geq3$ and $q$. We give an upper bound for anti-canonical volumes of $d$-dimensional $\frac{1}{q}$-lc toric Fano varieties, which corresponds to an upper bound for the dual normalized volumes of the associated $d$-dimensional $\frac{1}{q}$-lc Fano polytopes. And we also construct examples to show that these upper bounds are optimal. Besides, we provide an optimal upper bound for volumes of $d$-dimensional lattice simplices $S$ such that $\frac{1}{q}S$ has exactly one interior lattice point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19870 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal upper bounds for anti-canonical volumes of singular toric Fano varieties Zou, Yu Algebraic Geometry 14J45(Primary) 14M25, 52B20(Secondary) Fix two positive integers $d\geq3$ and $q$. We give an upper bound for anti-canonical volumes of $d$-dimensional $\frac{1}{q}$-lc toric Fano varieties, which corresponds to an upper bound for the dual normalized volumes of the associated $d$-dimensional $\frac{1}{q}$-lc Fano polytopes. And we also construct examples to show that these upper bounds are optimal. Besides, we provide an optimal upper bound for volumes of $d$-dimensional lattice simplices $S$ such that $\frac{1}{q}S$ has exactly one interior lattice point. |
| title | Optimal upper bounds for anti-canonical volumes of singular toric Fano varieties |
| topic | Algebraic Geometry 14J45(Primary) 14M25, 52B20(Secondary) |
| url | https://arxiv.org/abs/2407.19870 |