Kahler metrics on toric orbifolds
Abstract
A theorem of E.Lerman and S.Tolman, generalizing a result of T.Delzant, states that compact symplectic toric orbifolds are classified by their moment polytopes, together with a positive integer label attached to each of their facets. In this paper we use this result, and the existence of "global" actionangle coordinates, to give an effective parametrization of all compatible toric complex structures on a compact symplectic toric orbifold, by means of smooth functions on the corresponding moment polytope. This is equivalent to parametrizing all toric Kahler metrics and generalizes an analogous result for toric manifolds. A simple explicit description of interesting families of extremal Kahler metrics, arising from recent work of R.Bryant, is given as an application of the approach in this paper. The fact that in dimension four these metrics are selfdual and conformally Einstein is also discussed. This gives rise in particular to a one parameter family of selfdual Einstein metrics connecting the well known EguchiHanson and TaubNUT metrics.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2001
 arXiv:
 arXiv:math/0105112
 Bibcode:
 2001math......5112A
 Keywords:

 Differential Geometry;
 Symplectic Geometry;
 53C55
 EPrint:
 26 pages, 2 figures