vix.ing · top · new · best · stats · spec

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

2024/07/29 by Y. Zou, Zou, Yu
Mathematics · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2407.19870

Abstract

Fix two positive integers d≥3 and q. We give an upper bound for anti-canonical volumes of d-dimensional (1)/(q)-lc toric Fano varieties, which corresponds to an upper bound for the dual normalized volumes of the associated d-dimensional (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 (1)/(q)S has exactly one interior lattice point.

Related