Toric graph associahedra and compactifications of M0,n

Rodrigo Ferreira da Rosa; David Jensen; Dhruv Ranganathan

doi:10.1007/s10801-015-0629-7

Toric graph associahedra and compactifications of M_0,n

Rodrigo Ferreira da Rosa, David Jensen, Dhruv Ranganathan

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

To any graph G, one can associate a toric variety X(PG), 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(PG) 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.

Original language	English
Pages (from-to)	139-151
Number of pages	13
Journal	Journal of Algebraic Combinatorics
Volume	43
Issue number	1
DOIs	https://doi.org/10.1007/s10801-015-0629-7
State	Published - Feb 1 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media New York.

Funding

This work was completed as part of the 2014 Summer Undergraduate Mathematics Research at Yale (SUMRY) program, where the first author was a participant and the second and third authors were mentors. We are grateful to all involved in the SUMRY program for the vibrant research community that they helped create. It is a pleasure to thank Dagan Karp, who actively collaborated with the third when the ideas in the present text were at their early stages. We thank Satyan Devadoss for his encouragement, as well as permission to include Fig. from []. Finally, we thank the referee for their careful reading and comments. The authors were supported by NSF Grant CAREER DMS-1149054 (PI: Sam Payne).

Funders	Funder number
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-1149054

Keywords

Graph associahedra
Hassett space
Moduli space of curves
Permutohedron
Toric variety

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s10801-015-0629-7

Cite this

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abstract = "To any graph G, one can associate a toric variety X(PG), 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(PG) is isomorphic to a Hassett compactification of M0,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.",

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