The Koszul property of pinched Veronese varieties

Abstract

Let $K$ be an arbitrary field. Let $n,d\ge 2$ be positive integers. Let $V(n,d)$ be the set of all lattice points $\mathbf{b}=(b_1,...,b_n)$ in ${\mathbb{N}}^n$ such that ${\sum }_{i=1}^n{b}_i=d$. Let $\Gamma =V(n,d)\setminus \{\mathbf{a}\}$ for some element $\mathbf{a}\in V(n,d)$. In this paper we prove that the semigroup ring $K[\Gamma ]$ is Koszul unless $d\ge 3$ and $\mathbf{a}=(0,...,0,2,d-2)$ or one of its permutations. This generalizes results of Caviglia, Conca, and Tancer.

arXiv comment12 pages

References in corpus (1)

• Shellability of the higher pinched Veronese posets

Cited by in corpus (1)

• Shellability of the higher pinched Veronese posets