In 1978 Yau proposed a noncompact version of Calabi's conjecture: Given a compact complex space X and an anticanonical divisor D in X, does the complement X\D admit complete Ricci-flat Kähler metrics? Conversely, is it true that any complete Ricci-flat Kähler manifold can be written as X\D in this way? I will survey some recent work in this direction (partly joint with R. Conlon, M. Haskins, and J. Nordström) dealing with questions of existence, asymptotic properties, uniqueness, and classification of such metrics in various special situations.
Complete Ricci-flat Kähler manifolds
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Nom de l'orateur
Hans-Joachim Hein
Etablissement de l'orateur
Imperial College
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