Moduli spaces of toric manifolds

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.

To appear in Geometriae Dedicata, minor changes to previous version, 19 pages, 6 figures

References in corpus (2)

• Semitoric integrable systems on symplectic 4-manifolds
• Symplectic geometry on moduli spaces of J-holomorphic curves

Cited by in corpus (6)

• Semitoric systems of non-simple type
• The generalized Pythagorean theorem on the compactifications of certain dually flat spaces via toric geometry
• Classifying Toric and Semitoric Fans by Lifting Equations from ${\mathrm{SL}}_2(\mathbb{Z})$
• Minimal models of compact symplectic semitoric manifolds
• Moduli spaces of Delzant polytopes and symplectic toric manifolds
• Distance functions on convex bodies and symplectic toric manifolds