0046-5755
Moduli spaces of toric manifolds
Pelayo
A.
Inst Adv Study, Sch Math, Princeton, NJ 08540 USA
Pires
A. R.
Cornell Univ, Dept Math, Ithaca, NY 14853 USA
Ratiu
T. S.
Ecole Polytech Fed Lausanne, Sect Math, Stn 8, CH-1015 Lausanne, Switzerland
Sabatini
S.
Ecole Polytech Fed Lausanne, Sect Math, Stn 8, CH-1015 Lausanne, Switzerland
2014
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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