Degenerating Kähler–Einstein cones, locally symmetric cusps, and the Tian–Yau metric

Biquard, Olivier; Guenancia, Henri

doi:10.1007/s00222-022-01138-5

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2023

2024

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Cited by 2 publications

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“…If one wishes to extend the picture to manifolds without symmetries, a natural replacement to Stenzel's metrics is provided by Tian–Yau's asymptotically conical complete Ricci flat Kähler metrics on the complement of a divisor [12]. Biquard and Guenancia informed the author that they studied this problem in general by gluing techniques (with a strategy analogous to [3]), obtaining a wide generalization.…”

Section: Introductionmentioning

confidence: 99%

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

Delcroix

2024

Bulletin of London Math Soc

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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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Section: Introductionmentioning

confidence: 99%