On the Gauss Algebra of Toric Algebras
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Date
20180425MFO Scientific Program
Research in Pairs 2018Series
Oberwolfach Preprints;2018,07Author
Herzog, Jürgen
Jafari, Raheleh
Nasrollah Nejad, Abbas
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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 $\mathbb{G}(A)$ of $A$ is generated by monomials of degree $(r1)d$ in $S$. We describe the generators and the structure of $\mathbb{G}(A)$, 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 $\mathbb{G}(A)$ is bounded by the complexity of the graph $G$.
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