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arXiv · 2010.13720

A regular unimodular triangulation of reflexive 2-supported weighted projective space simplices

Benjamin Braun·Derek Hanely
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Abstract

For each integer partition $\mathbf{q}$ with $d$ parts, we denote by $Δ_{(1,\mathbf{q})}$ the lattice simplex obtained as the convex hull in $\mathbb{R}^d$ of the standard basis vectors along with the vector $-\mathbf{q}$. For $\mathbf{q}$ with two distinct parts such that $Δ_{(1,\mathbf{q})}$ is reflexive and has the integer decomposition property, we establish a characterization of the lattice points contained in $Δ_{(1,\mathbf{q})}$. We then construct a Gröbner basis with a squarefree initial ideal of the toric ideal defined by these simplices. This establishes the existence of a regular unimodular triangulation for reflexive 2-supported $Δ_{(1,\mathbf{q})}$ having the integer decomposition property.

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Benjamin Braun, Derek Hanely. 2020-10-26. A regular unimodular triangulation of reflexive 2-supported weighted projective space simplices. https://arxiv.org/abs/2010.13720

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