Gorenstein Semigroup Algebras of Weighted Trees

Details Gorenstein Semigroup Algebras of Weighted Trees Gorenstein Semigroup Algebras of Weighted Trees

2008-10-08

arxiv.org/abs/0810.1353v3

Mathematics

Commutative Algebra

11 Pages, 7 Figures, expanded proof of proposition 3.2

Scientific paper

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 Pl\"ucker 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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