Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
Riemannian geometry of Kahler-Einstein currents II: an analytic proof of Kawamata's base point free theorem
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发表时间：
2014-09
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通讯作者：
Jian Song
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作者：
Jian Song
Kawamata证明了射影流形的正则丛如果大且nef，则为半充足。我们利用 Ricci 流、黎曼流形的简并和 $L^2$ 理论给出了解析证明。结合我们早期的结果，我们在规范模型上构建了具有全局黎曼结构的独特奇异卡勒-爱因斯坦度量。我们的方法可以被视为具有规范卡勒度量的奇异度量空间上的 Kodaira 嵌入定理。
It is proved by Kawamata that the canonical bundle of a projective manifold is semi-ample if it is big and nef. We give an analytic proof using the Ricci flow, degeneration of Riemannian manifolds and $L^2$-theory. Combined with our earlier results, we construct unique singular Kahler-Einstein metrics with a global Riemannian structure on canonical models. Our approach can be viewed as the Kodaira embedding theorem on singular metric spaces with canonical Kahler metrics.