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

2017/08/09 by Aleksei Golota, Golota, Aleksei
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1708.02866

8 pages, minor corrections, Proposition 3.2.1 attributed to Campana-Paun, acknowledgement added

arxiv created 2017/09/03 · arxiv updated 2017/09/05

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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