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Kähler-Einstein potential on simple polytope

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  • UserÉveline Legendre (Toulouse)
  • ClockWednesday 06 March 2013, 14:15-15:15
  • HouseMR 13, CMS.

If you have a question about this talk, please contact Dr. J Ross.

I will explain how any simple polytope can be labelled to satisfy the combinatorial condition of being monotone with a vanishing Futaki invariant. Using the Wang-Zhu theorem for orbifolds, we obtain that every lattice simple polytope is the moment polytope of a Kähler-Einstein orbifold unique up to covering and dilatation. Extending Donaldson’s alternative proof of the Wang-Zhu theorem to any simple polytope, we get that they all carry a Kähler-Einstein potential. In the Delzant case, this potential gives a Kähler-Einstein metric (with conical singularity along a divisor) on the associated (smooth) symplectic toric manifold.

This talk is part of the Algebraic Geometry Seminar series.

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