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Effective bounds of linear series on algebraic varieties and arithmetic varieties

Yuan, X.; Zhang, T.

Effective bounds of linear series on algebraic varieties and arithmetic varieties Thumbnail


Authors

X. Yuan

T. Zhang



Abstract

In this paper, we prove effective upper bounds for effective sections of line bundles on projective varieties and hermitian line bundles on arithmetic varieties in terms of the volumes. They are effective versions of the Hilbert–Samuel formula and the arithmetic Hilbert–Samuel formula. The treatments are high-dimensional generalizations of [Duke. Math. J. 162 (2013), 1723–1770] and [`Relative Noether inequality on fibered surfaces', preprint 2013]. Similar results are obtained independently by Huayi Chen [`Majorations explicites de fonctions de Hilbert–Samuel géométrique et arithmétique', preprint 2014] with less explicit error terms.

Journal Article Type Article
Acceptance Date Feb 12, 2015
Online Publication Date Jul 7, 2015
Publication Date Mar 1, 2018
Deposit Date May 9, 2017
Publicly Available Date Jul 21, 2017
Journal Journal für die reine und angewandte Mathematik
Print ISSN 0075-4102
Electronic ISSN 1435-5345
Publisher De Gruyter
Peer Reviewed Peer Reviewed
Volume 2018
Issue 736
Pages 255-284
DOI https://doi.org/10.1515/crelle-2015-0025
Public URL https://durham-repository.worktribe.com/output/1388008

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Advance online version The final publication is available at www.degruyter.com





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