Geodesic
Toric graph associahedra and compactifications of $M_{0,n}$
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 139-151.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 polytopes of these toric varieties are the graph associahedra, 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 with the permutohedron.
Classification : 14H10, 14M25, 14D20, 52B05
Keywords: graph associahedra, permutohedron, Hassett space, moduli space of curves, toric variety 
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     title = {Toric graph associahedra and compactifications of $M_{0,n}$},
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Ferreira da Rosa, Rodrigo; Jensen, David; Ranganathan, Dhruv. Toric graph associahedra and compactifications of $M_{0,n}$. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 139-151. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a4/