On the maximum dual volume of a canonical Fano polytope
Forum of Mathematics, Sigma, Tome 10 (2022)
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We give an upper bound on the volume $\operatorname {vol}(P^*)$ of a polytope $P^*$ dual to a d-dimensional lattice polytope P with exactly one interior lattice point in each dimension d. This bound, expressed in terms of the Sylvester sequence, is sharp and achieved by the dual to a particular reflexive simplex. Our result implies a sharp upper bound on the volume of a d-dimensional reflexive polytope. Translated into toric geometry, this gives a sharp upper bound on the anti-canonical degree $(-K_X)^d$ of a d-dimensional Fano toric variety X with at worst canonical singularities.
@article{10_1017_fms_2022_93,
author = {Gabriele Balletti and Alexander M. Kasprzyk and Benjamin Nill},
title = {On the maximum dual volume of a canonical {Fano} polytope},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.93},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.93/}
}
TY - JOUR AU - Gabriele Balletti AU - Alexander M. Kasprzyk AU - Benjamin Nill TI - On the maximum dual volume of a canonical Fano polytope JO - Forum of Mathematics, Sigma PY - 2022 VL - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.93/ DO - 10.1017/fms.2022.93 LA - en ID - 10_1017_fms_2022_93 ER -
%0 Journal Article %A Gabriele Balletti %A Alexander M. Kasprzyk %A Benjamin Nill %T On the maximum dual volume of a canonical Fano polytope %J Forum of Mathematics, Sigma %D 2022 %V 10 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.93/ %R 10.1017/fms.2022.93 %G en %F 10_1017_fms_2022_93
Gabriele Balletti; Alexander M. Kasprzyk; Benjamin Nill. On the maximum dual volume of a canonical Fano polytope. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.93
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