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Moduli spaces of toric manifolds

Pelayo, Á. ; Pires, A. ; Ratiu, T. ; Sabatini, S.

In: Geometriae Dedicata, 2014, vol. 169, no. 1, p. 323-341

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    Title
    • Moduli spaces of toric manifolds
    Author
    • Pelayo, Á.. School of Mathematics, Institute of Advanced Study, Einstein Drive, 08540, Princeton, NJ, USA
    • Pires, A.. Department of Mathematics, Cornell University, 310 Malott Hall, 14853-4201, Ithaca, NY, USA
    • Ratiu, T.. Section de Mathématiques and Bernoulli Center, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015, Lausanne, Switzerland
    • Sabatini, S.. Section de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015, Lausanne, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:326094
    Summary
    We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance is related to the Duistermaat-Heckman measure and the Hausdorff metric. While the moduli space, its topology and metric, may be constructed in any dimension, the tools we use in the proofs are four-dimensional, and hence so is our main result.