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arXiv · 1207.0092

Moduli spaces of toric manifolds

Álvaro Pelayo·Ana Rita Pires·Tudor S. Ratiu·Silvia Sabatini
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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.

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Álvaro Pelayo, Ana Rita Pires, Tudor S. Ratiu, Silvia Sabatini. 2013-04-30. Moduli spaces of toric manifolds. https://doi.org/10.1007/s10711-013-9858-x

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