RC-positive metrics on rationally connected manifolds

In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric $\omega $ such that $(T_X,\omega )$ is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective manifold X is rationally connected, then ther...

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Bibliographic Details
Published in:Forum of Mathematics, Sigma
Main Author: Xiaokui Yang
Format: Article
Language:English
Published: Cambridge University Press 2020-01-01
Subjects:
53C55
14E08
14F17
32L20
rationally connected
RC-positivity
vanishing theorem
Online Access:https://www.cambridge.org/core/product/identifier/S2050509420000328/type/journal_article
Description
Summary:In this paper, we prove that if a compact Kähler manifold X has a smooth Hermitian metric $\omega $ such that $(T_X,\omega )$ is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective manifold X is rationally connected, then there exists a uniformly RC-positive complex Finsler metric on $T_X$ .
ISSN:2050-5094

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