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Vestislav Apostolov (Université du Québec à Montréal)
Tuesday 10 April 2012, 11:30-12:30
Ambitoric structures and extremal Kahler orbi-surfaces with b_2(M)=2.
- 👤 Speaker: Vestislav Apostolov (Université du Québec à Montréal)
- 📅 Date & Time: Tuesday 10 April 2012, 11:30 - 12:30
- 📍 Venue: MR2
Abstract
I will discuss an explicit resolution of the existence problem for extremal Kahler metrics on toric 4-orbifolds $M$ with second Betti number equal to 2.
More precisely, I will show that $M$ admits such a metric if and only if its rational Delzant polytope (which is a labelled quadrilateral) is K- polystable in the relative, toric sense (as studied by S. Donaldson, G. Sz\’ekelyhidi et al.). Furthermore, in this case, the extremal Kahler metric is ambitoric, i.e., compatible with a conformally equivalent, oppositely oriented toric Kahler metric, which turns out also to be extremal.
Among the explicit extremal Kahler metrics obtained, there are conformally Einstein examples which are Riemannian analogues of the exact solutions of the Einstein equations in General Relativity, found by R. Debever, N. Kamran, and R. McLenaghan. This is a joint work with D. Calderbank and P. Gauduchon.
Series This talk is part of the Workshop on Kahler Geometry series.
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