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arXiv · 1708.02866

On negativity of total $k$-jet curvature and ampleness of the canonical bundle

Aleksei Golota
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Abstract

A celebrated conjecture of Kobayashi and Lang says that the canonical line bundle $K_X$ of a Kobayashi hyperbolic compact complex manifold $X$ is ample. In this note we prove that $K_X$ is ample if $X$ is projective and satisfies a stronger condition of nondegenerate negative total $k$-jet curvature. We use positivity of direct image sheaves and decomposition of jets in order to produce pluridifferentials on $X$.

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Aleksei Golota. 2017-08-09. On negativity of total $k$-jet curvature and ampleness of the canonical bundle. https://arxiv.org/abs/1708.02866

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