Moduli spaces of toric manifolds
\'Alvaro Pelayo, Ana Rita Pires, Tudor S. Ratiu, Silvia Sabatini

TL;DR
This paper introduces a new metric on the moduli space of four-dimensional symplectic toric manifolds, analyzing its topological properties such as connectedness, compactness, and completeness.
Contribution
It constructs a distance based on the Duistermaat-Heckman measure and Hausdorff metric specifically for four-dimensional cases, providing new insights into the space's topology.
Findings
The moduli space is path-connected.
The space is compact.
The space is complete.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
