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arXiv · 1309.3033

The Koszul property of pinched Veronese varieties

Thanh Vu
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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.

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Thanh Vu. 2013-09-12. The Koszul property of pinched Veronese varieties. https://arxiv.org/abs/1309.3033

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