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2019 Effective generation and twisted weak positivity of direct images
Yajnaseni Dutta, Takumi Murayama
Algebra Number Theory 13(2): 425-454 (2019). DOI: 10.2140/ant.2019.13.425

Abstract

We study pushforwards of log pluricanonical bundles on projective log canonical pairs (Y,Δ) over the complex numbers, partially answering a Fujita-type conjecture due to Popa and Schnell in the log canonical setting. We show two effective global generation results. First, when Y surjects onto a projective variety, we show a quadratic bound for generic generation for twists by big and nef line bundles. Second, when Y is fibered over a smooth projective variety, we show a linear bound for twists by ample line bundles. These results additionally give effective nonvanishing statements. We also prove an effective weak positivity statement for log pluricanonical bundles in this setting, which may be of independent interest. In each context we indicate over which loci positivity holds. Finally, using the description of such loci, we show an effective vanishing theorem for pushforwards of certain log-sheaves under smooth morphisms.

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Yajnaseni Dutta. Takumi Murayama. "Effective generation and twisted weak positivity of direct images." Algebra Number Theory 13 (2) 425 - 454, 2019. https://doi.org/10.2140/ant.2019.13.425

Information

Received: 6 February 2018; Revised: 23 October 2018; Accepted: 24 November 2018; Published: 2019
First available in Project Euclid: 26 March 2019

zbMATH: 07042064
MathSciNet: MR3927051
Digital Object Identifier: 10.2140/ant.2019.13.425

Subjects:
Primary: 14C20
Secondary: 14D06 , 14E30 , 14F05 , 14J17 , 14Q20

Keywords: effective results , Fujita's conjecture , pluricanonical bundles , Seshadri constants , weak positivity

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2019
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