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Ben McKay
Ben McKay
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Let $π:X→Δ$ be a family of compact complex manifolds such that the fibre $X_t:=π^{−1}(t)$ admitadmits a Kaehler-Einstein metric of negative Ricci curvature for all $t≠0$. Then does the special fiber $X_0:=π^{−1}(0)$ also admit a Kaehler-Einstein metric of negative Ricci curvature?

Let $π:X→Δ$ be a family of compact complex manifolds such that the fibre $X_t:=π^{−1}(t)$ admit Kaehler-Einstein metric of negative Ricci curvature for all $t≠0$. Then the special fiber $X_0:=π^{−1}(0)$ also admit Kaehler-Einstein metric of negative Ricci curvature?

Let $π:X→Δ$ be a family of compact complex manifolds such that the fibre $X_t:=π^{−1}(t)$ admits a Kaehler-Einstein metric of negative Ricci curvature for all $t≠0$. Then does the special fiber $X_0:=π^{−1}(0)$ also admit a Kaehler-Einstein metric of negative Ricci curvature?

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Dima
Dima
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Degeneration of Kaehler-Einstein metric of negative Ricci curvature

Let $π:X→Δ$ be a family of compact complex manifolds such that the fibre $X_t:=π^{−1}(t)$ admit Kaehler-Einstein metric of negative Ricci curvature for all $t≠0$. Then the special fiber $X_0:=π^{−1}(0)$ also admit Kaehler-Einstein metric of negative Ricci curvature?