AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Electronic Research Archive Article
PDF (621.7 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Strict Arakelov inequality for a family of varieties of general type

Xin Lu1, Jinbang Yang2, Kang Zuo3( )
School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, No. 500 Dongchuan Road, Shanghai 200241, China
Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China
Institut für Mathematik, Universität Mainz, Mainz 55099, Germany
Show Author Information

Abstract

Let f:X→Y be a semistable non-isotrivial family of n-folds over a smooth projective curve with discriminant locus S⊆Y and with general fiber F of general type. We show the strict Arakelov inequality

deg⁡f∗ωX/Yνrankf∗ωX/Yν<nν2⋅deg⁡ΩY1(log⁡S),

for all ν∈N such that the ν-th pluricanonical linear system |ωFν| is birational. This answers a question asked by Möller, Viehweg and the third named author [1].

Keywords

Arakelov inequalityfamily

References

【1】
【1】
 
 
Crossref Google Scholar
Electronic Research Archive
Volume 30 Issue 7,
July 2022
Pages 2643-2662
DOI: 10.3934/era.2022135

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Lu X, Yang J, Zuo K. Strict Arakelov inequality for a family of varieties of general type. Electronic Research Archive, 2022, 30(7): 2643-2662. https://doi.org/10.3934/era.2022135

0

Views

0

Downloads

0

Crossref

0

Web of Science

1

Scopus
Received: 13 April 2021
Revised: 26 December 2021
Accepted: 03 January 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)