Geometriae Dedicata

, Volume 169, Issue 1, pp 323–341 | Cite as

Moduli spaces of toric manifolds

  • Á. Pelayo
  • A. R. Pires
  • T. S. Ratiu
  • S. Sabatini
Original Paper

Abstract

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.

Keywords

Toric manifold Delzant polytope Moduli space  Metric space 

Mathematics Subject Classification (2000)

MSC 53D20 MSC 53D05 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Á. Pelayo
    • 1
    • 2
  • A. R. Pires
    • 3
  • T. S. Ratiu
    • 4
  • S. Sabatini
    • 5
  1. 1.School of MathematicsInstitute of Advanced StudyPrincetonUSA
  2. 2.Mathematics DepartmentWashington UniversitySt. LouisUSA
  3. 3.Department of MathematicsCornell UniversityIthacaUSA
  4. 4.Section de Mathématiques and Bernoulli CenterLausanneSwitzerland
  5. 5.Section de MathématiquesLausanneSwitzerland

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