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arXiv · 1804.07971

On the Gauss algebra of toric algebras

Jürgen Herzog·Raheleh Jafari·Abbas Nasrollah Nejad
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Abstract

Let $A$ be a $K$-subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\GG(A)$ of $A$ is generated by monomials of degree $(r-1)d$ in $S$. We describe the generators and the structure of $\GG(A)$, when $A$ is a Borel fixed algebra, a squarefree Veronese algebra, generated in degree $2$, or the edge ring of a bipartite graph with at least one loop. For a bipartite graph $G$ with one loop, the embedding dimension of $\GG(A)$ is bounded by the complexity of the graph $G$.

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Jürgen Herzog, Raheleh Jafari, Abbas Nasrollah Nejad. 2018-04-21. On the Gauss algebra of toric algebras. https://arxiv.org/abs/1804.07971

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