Steady gradient Kähler-Ricci solitons

Mercredi 25 novembre 16:00-18:00 - Alix Deruelle - IMJ-PRG

Résumé : Steady gradient Kähler-Ricci solitons are fixed points of the Kähler-Ricci flow which only evolve under the action of biholomorphisms generated by a real holomorphic vector field. The formation of such singularities along the Ricci flow is known to be rather slow and this makes them hard to detect. We show that there is a unique steady gradient Kähler-Ricci soliton in each Kähler class of an equivariant crepant resolution of a Calabi-Yau cone. To do so, we solve a weighted complex Monge-Ampère equation via a continuity method. Our construction is based on an ansatz due to Cao in the 90’s which has been revived by Biquard-MacBeth in 2017.

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