Gorenstein semigroup algebras of weighted trees and ordered points on the projective line (Q448398)

The author studies a class of semigroups \(S_\tau (r)\) associated to a trivalent tree \(\tau \) and to a polytope \({\mathcal P}_\tau (r)\). The main result characterizes when \(K[S_\tau (r)]\) is Gorenstein. The algebras \(K[S_\tau (r)]\) arise as toric degenerations of projective coordinate rings \(C[M_r]\) of moduli of weighted points on the projective line. As a corollary the author finds exactly when \(C[M_r]\) is Gorenstein.