On Nonvanishing for uniruled log canonical pairs

Vladimir Lazić; Fanjun Meng; Vladimir Lazić; Fanjun Meng

doi:10.3934/era.2021039

Electronic Research Archive

2021, Volume 29, Issue 5: 3297-3308. doi: 10.3934/era.2021039

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On Nonvanishing for uniruled log canonical pairs

Vladimir Lazić ^{1
,
,},
Fanjun Meng ^{2
,}

1.
Fachrichtung Mathematik, Campus, Gebäude E2.4, Universität des Saarlandes, 66123 Saarbrücken, Germany
2.
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA

Received: 01 November 2020 Revised: 01 April 2021 Published: 26 May 2021
Primary: 14E30

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 $.
- Good minimal models,
- Minimal Model Program,
- Nonvanishing conjecture
Citation: Vladimir Lazić, Fanjun Meng. On Nonvanishing for uniruled log canonical pairs[J]. Electronic Research Archive, 2021, 29(5): 3297-3308. doi: 10.3934/era.2021039

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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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