Gorenstein Semigroup Algebras of Weighted Trees

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.

11 Pages, 7 Figures, expanded proof of proposition 3.2

References in corpus (3)

• The projective invariants of ordered points on the line
• The Toric Geometry of Triangulated Polygons in Euclidean Space
• Presentations of Semigroup Algebras of Weighted Trees