Degenerations of conical Kähler-Einstein metrics

Degenerations of conical Kähler-Einstein metrics

Olivier Biquard, Sorbonne Université

Online Talk

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We study two cases of degenerations of Kähler-Einstein metrics with a conical angle around a divisor going to zero. The first case is that of a locally symmetric space and we show convergence to the locally symmetric metric, with further asymptotics in the case of a ball quotient. The second case is that of an anticanonical divisor in a Fano manifold. We answer a question of Donaldson by showing that a rescaled metric converges to the complete, Ricci flat Tian-Yau metric in the complement of the divisor.

Joint work with Henri Guenancia.