Strict Arakelov inequality for a family of varieties of general type

Xin Lu; Jinbang Yang; Kang Zuo

doi:10.3934/era.2022135

Strict Arakelov inequality for a family of varieties of general type

Xin Lu, Jinbang Yang, Kang Zuo

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let f: X Y be a semistable non-isotrivial family of n-folds over a smooth projective curve with discriminant locus S (Formula presented) Y and with general fiber F of general type. We show the strict Arakelov inequality (Formula presented) for all v (Formula presented) (Formula presented) such that the v-th pluricanonical linear system |(Formula presented)| is birational. This answers a question asked by Möller, Viehweg and the third named author [1].

Original language	English
Pages (from-to)	2643-2662
Number of pages	20
Journal	Electronic Research Archive
Volume	30
Issue number	7
DOIs	https://doi.org/10.3934/era.2022135
State	Published - 2022

Keywords

Arakelov inequality
family

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10.3934/era.2022135

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abstract = "Let f: X Y be a semistable non-isotrivial family of n-folds over a smooth projective curve with discriminant locus S (Formula presented) Y and with general fiber F of general type. We show the strict Arakelov inequality (Formula presented) for all v (Formula presented) (Formula presented) such that the v-th pluricanonical linear system |(Formula presented)| is birational. This answers a question asked by M{\"o}ller, Viehweg and the third named author [1].",

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author = "Xin Lu and Jinbang Yang and Kang Zuo",

year = "2022",

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AU - Lu, Xin

AU - Yang, Jinbang

AU - Zuo, Kang

PY - 2022

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N2 - Let f: X Y be a semistable non-isotrivial family of n-folds over a smooth projective curve with discriminant locus S (Formula presented) Y and with general fiber F of general type. We show the strict Arakelov inequality (Formula presented) for all v (Formula presented) (Formula presented) such that the v-th pluricanonical linear system |(Formula presented)| is birational. This answers a question asked by Möller, Viehweg and the third named author [1].

AB - Let f: X Y be a semistable non-isotrivial family of n-folds over a smooth projective curve with discriminant locus S (Formula presented) Y and with general fiber F of general type. We show the strict Arakelov inequality (Formula presented) for all v (Formula presented) (Formula presented) such that the v-th pluricanonical linear system |(Formula presented)| is birational. This answers a question asked by Möller, Viehweg and the third named author [1].

KW - Arakelov inequality

KW - family

UR - https://www.scopus.com/pages/publications/85131439401

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DO - 10.3934/era.2022135

M3 - 文章

AN - SCOPUS:85131439401

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JO - Electronic Research Archive

JF - Electronic Research Archive

IS - 7

ER -

Strict Arakelov inequality for a family of varieties of general type

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Keywords

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