Strict Arakelov inequality for a family of varieties of general type-Reference-Cited by-同舟云学术

Strict Arakelov inequality for a family of varieties of general type

Published:2022 Issue:7 Volume:30 Page:2643-2662
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Lu Xin¹,Yang Jinbang²,Zuo Kang³

Affiliation:

1. School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, No. 500 Dongchuan Road, Shanghai 200241, China

2. Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China

3. Institut für Mathematik, Universität Mainz, Mainz 55099, Germany

Abstract

<abstract>Let $ f:\, X\to Y $ be a semistable non-isotrivial family of $ n $-folds over a smooth projective curve with discriminant locus $ S \subseteq Y $ and with general fiber $ F $ of general type. We show the strict Arakelov inequality <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ {\deg f_*\omega_{X/Y}^\nu \over {{{\rm{rank\,}}}} f_*\omega_{X/Y}^\nu} < {n\nu\over 2}\cdot\deg\Omega^1_Y(\log S), $\end{document} </tex-math></disp-formula> for all $ \nu\in \mathbb N $ such that the $ \nu $-th pluricanonical linear system $ |\omega^\nu_F| $ is birational. This answers a question asked by Möller, Viehweg and the third named author [<xref ref-type="bibr" rid="b1">1</xref>].</abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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