Effective bounds of linear series on algebraic varieties and arithmetic varieties

Yuan, X.; Zhang, T.

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.

Citation

Yuan, X., & Zhang, T. (2018). Effective bounds of linear series on algebraic varieties and arithmetic varieties. Journal für die reine und angewandte Mathematik, 2018(736), 255-284. https://doi.org/10.1515/crelle-2015-0025

• 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