Ambitoric structures and extremal Kahler orbi-surfaces with b_2(M)=2 (Vestislav Apostolov)
Duration: 1 hour 1 min 30 secs
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About this item
| Description: | (No description) |
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| Created: | 2012-04-23 10:26 | ||
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| Collection: | Workshop on Kahler Geometry | ||
| Publisher: | University of Cambridge | ||
| Copyright: | Dr J. Ross | ||
| Language: | eng (English) | ||
| Credits: |
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| 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. Szekelyhidi 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. |
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