Toric graph associahedra and compactifications of $M_{0,n}$

Abstract

To any graph $G$ one can associate a toric variety $X(\mathcal{P}G)$, obtained as a blowup of projective space along coordinate subspaces corresponding to connected subgraphs of $G$. The polytope of this toric variety is the graph associahedron of $G$, a class of polytopes that includes the permutohedron, associahedron, and stellahedron. We show that the space $X(\mathcal{P}G)$ is isomorphic to a Hassett compactification of $M_{0,n}$ precisely when $G$ is an iterated cone over a discrete set. This may be viewed as a generalization of the well-known fact that the Losev--Manin moduli space is isomorphic to the toric variety associated to the permutohedron.

11 pages, 4 figures. Final Version: Minor clarifications. To appear in Journal of Algebraic Combinatorics

References in corpus (1)

• The tropicalization of the moduli space of curves

Cited by in corpus (1)

• Birational contractions of ${\overline{\mathrm{M}}}_{0,n}$ and combinatorics of extremal assignments