Presentations of Semigroup Algebras of Weighted Trees

Abstract

We find presentations for subalgebras of invariants of the coordinate algebras of binary symmetric models of phylogenetic trees studied by Buczynska and Wisniewski in \cite{BW}. These algebras arise as toric degenerations of rings of global sections of weight varieties of the Grassmanian of two planes associated to the Plücker embedding, and as toric degenerations of rings of invariants of Cox-Nagata rings.

17 pages; 16 figures; Shortened proof of Theorems 2.2 and 2.4, changed abstract

References in corpus (2)

• The projective invariants of ordered points on the line
• The Toric Geometry of Triangulated Polygons in Euclidean Space

Cited by in corpus (8)

• Coordinate rings for the moduli of $SL_2(\C)$ quasi-parabolic principal bundles on a curve and toric fiber products
• Toric Degenerations and tropical geometry of branching algebras
• The algebra of $S{L}_3(\mathbb{C})$ conformal blocks
• Gorenstein Semigroup Algebras of Weighted Trees
• Blow-ups of ${\mathbb{P}}^{n-3}$ at $n$ points and spinor varieties
• Bounds on generators and relations for the algebra of $SL_2(\C)$ conformal blocks
• Conformal blocks, Berenstein-Zelevinsky triangles and group-based models
• The ideal of relations for the ring of invariants of n points on the line