Pelayo, A.
Pires, A. R.
Ratiu, T. S.
Sabatini, S.
Moduli spaces of toric manifolds
Geometriae Dedicata
0046-5755
10.1007/s10711-013-9858-x
169
1
323-341
19
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.
Toric manifold;
Delzant polytope;
Moduli space;
Metric space;
Springer Verlag
Dordrecht
2014