Singular metrics and a conjecture by Campana and Peternell

2022/02/02 by Schnell, Christian · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.01295

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.

Cited by

• Note on Iitaka Conjecture C_n,m

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