Toric ideals of Minkowski sums of unit simplices
Combinatorics
2020-10-16 v2 Commutative Algebra
Algebraic Geometry
Abstract
In this paper, we discuss the toric ideals of Minkowski sums of unit simplices. More precisely, we prove that the toric ideal of Minkowski sum of unit simplices has a squarefree initial ideal and is generated by quadratic binomials. Moreover, we also prove that Minkowski sums of unit simplices have the integer decomposition property. Those results are a partial contribution to Oda conjecture and B{\o}gvad conjecture.
Keywords
Cite
@article{arxiv.1908.01415,
title = {Toric ideals of Minkowski sums of unit simplices},
author = {Akihiro Higashitani and Hidefumi Ohsugi},
journal= {arXiv preprint arXiv:1908.01415},
year = {2020}
}
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8 pages