Lazić, Vladimir and Peternell, Thomas - Abundance for varieties with many differential forms

epiga:3867 - Épijournal de Géométrie Algébrique, February 13, 2018, Volume 2
Abundance for varieties with many differential forms

Authors: Lazić, Vladimir and Peternell, Thomas

We prove that the abundance conjecture holds on a variety $X$ with mild singularities if $X$ has many reflexive differential forms with coefficients in pluricanonical bundles, assuming the Minimal Model Program in lower dimensions. This implies, for instance, that under this condition, hermitian semipositive canonical divisors are almost always semiample, and that klt pairs whose underlying variety is uniruled have good models in many circumstances. When the numerical dimension of $K_X$ is $1$, our results hold unconditionally in every dimension. We also treat a related problem on the semiampleness of nef line bundles on Calabi-Yau varieties.

Volume: Volume 2
Published on: February 13, 2018
Submitted on: August 21, 2017
Keywords: Mathematics - Algebraic Geometry,14E30, 14F10