On Generalised Abundance, I

Thomas Peternell; Vladimir Lazi\'c

On Generalised Abundance, I

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arxiv 1808.00438 v2 pith:WJAA7G5P submitted 2018-08-01 math.AG

Vladimir Lazić , Thomas Peternell This is my paper · ORCID

classification math.AG

keywords conjectureabundancealgebraicbundlescentralconjecturesconnectiongeneralised

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The goal of this paper is to make a surprising connection between several central conjectures in algebraic geometry: the Nonvanishing Conjecture, the Abundance Conjecture, and the Semiampleness Conjecture for nef line bundles on K-trivial varieties.

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Abundance for uniruled pairs which are not rationally connected
math.AG 2019-08 accept novelty 8.0 of 10

Assuming the Minimal Model Program in dimension n-1, every uniruled but not rationally connected projective log canonical pair of dimension n with pseudoeffective log canonical divisor has a good model.

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