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Article Dans Une Revue Bulletin of the London Mathematical Society Année : 2024

Limits of conical Kähler-Einstein metrics on rank one horosymmetric spaces

Résumé

We consider families of conical Kähler-Einstein metrics on rank one horosymmetric Fano manifolds, with decreasing cone angles along a codimension one orbit. At the limit angle, which is positive, we show that the metrics, restricted to the complement of that orbit, converge to (the pull-back of) the Kähler-Einstein metric on the basis of the horosymmetric homogeneous space, which is a projective homogeneous space. Then we show that, on the symmetric space fibers, the rescaled metrics converge to Stenzel’s Ricci flat Kähler metric.
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hal-04258511 , version 1 (25-10-2023)

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Thibaut Delcroix. Limits of conical Kähler-Einstein metrics on rank one horosymmetric spaces. Bulletin of the London Mathematical Society, 2024, ⟨10.1112/blms.13069⟩. ⟨hal-04258511⟩
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