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arXiv · 2202.01295

Singular metrics and a conjecture by Campana and Peternell

Christian Schnell
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Abstract

A conjecture by Campana and Peternell says that if a positive multiple of $K_X$ is linearly equivalent to an effective divisor $D$ plus a pseudo-effective divisor, then the Kodaira dimension of $X$ should be at least as big as the Iitaka dimension of $D$. This is a very useful generalization of the non-vanishing conjecture (which is the case $D = 0$). We use recent work about singular metrics on pluri-adjoint bundles to show that the Campana-Peternell conjecture is almost equivalent to the non-vanishing conjecture.

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Christian Schnell. 2022-02-02. Singular metrics and a conjecture by Campana and Peternell. https://arxiv.org/abs/2202.01295

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