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arXiv · 2407.19870

Optimal upper bounds for anti-canonical volumes of singular toric Fano varieties

Yu Zou
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Abstract

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.

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Yu Zou. 2024-07-29. Optimal upper bounds for anti-canonical volumes of singular toric Fano varieties. https://arxiv.org/abs/2407.19870

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