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On Nonvanishing for uniruled log canonical pairs

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arxiv 1907.11991 v2 pith:BCWXCU3R submitted 2019-07-27 math.AG

Vladimir Lazić , Fanjun Meng This is my paper · ORCID
classification math.AG
keywords dimensionpairsprojectivecanonicalnonvanishingconjectureexistencegood
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abstract

We prove the Nonvanishing conjecture for uniruled projective log canonical pairs of dimension $n$, assuming the Nonvanishing conjecture for smooth projective varieties in dimension $n-1$. We also show that the existence of good minimal models for non-uniruled projective klt pairs in dimension $n$ implies the existence of good minimal models for projective log canonical pairs in dimension $n$.

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  1. 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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