Loading…

Effective generation and twisted weak positivity of direct images

In this paper, we study pushforwards of log pluricanonical bundles on projective log canonical pairs \((Y,\Delta)\) 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, whe...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: Dutta, Yajnaseni, Murayama, Takumi
Format: Article
Language:English
Subjects:
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we study pushforwards of log pluricanonical bundles on projective log canonical pairs \((Y,\Delta)\) 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 non-vanishing 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.
ISSN:2331-8422
DOI:10.48550/arxiv.1712.08723