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arXiv · 0810.1353

Gorenstein Semigroup Algebras of Weighted Trees

Christopher Manon
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Abstract

We classify exactly when the toric algebras $\C[S_{\tree}(\br)]$ are Gorenstein. These algebras arise as toric deformations of algebras of invariants of the Cox-Nagata ring of the blow-up of $n-1$ points on $\mathbb{P}^{n-3}$, or equivalently algebras of the ring of global sections for the Plücker embedding of weight varieties of the Grassmanian $Gr_2(\C^n)$, and algebras of global sections for embeddings of moduli of weighted points on $\mathbb{P}^1$. As a corollary, we find exactly when these families of rings are Gorenstein as well.

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Christopher Manon. 2011-05-11. Gorenstein Semigroup Algebras of Weighted Trees. https://doi.org/10.1016/j.jalgebra.2011.12.025

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