On the slope of hyperelliptic fibrations with positive relative irregularity

Xin Lu; Kang Zuo

doi:10.1090/tran6682

On the slope of hyperelliptic fibrations with positive relative irregularity

Xin Lu, Kang Zuo

School of Mathematical Sciences

Johannes Gutenberg University Mainz

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

13 Scopus citations

Abstract

Let f: S → B be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus g ≥ 2 with relative irregularity q_f. We show a sharp lower bound on the slope λ_f of f. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of λ_f as an increasing function of q_f in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if λ_f < 4.

Original language	English
Pages (from-to)	909-934
Number of pages	26
Journal	Transactions of the American Mathematical Society
Volume	369
Issue number	2
DOIs	https://doi.org/10.1090/tran6682
State	Published - 2017

Keywords

Fibrations
Relative irregularity
Slope inequality

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10.1090/tran6682

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title = "On the slope of hyperelliptic fibrations with positive relative irregularity",

abstract = "Let f: S → B be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus g ≥ 2 with relative irregularity qf. We show a sharp lower bound on the slope λf of f. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of λf as an increasing function of qf in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if λf < 4.",

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author = "Xin Lu and Kang Zuo",

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AU - Lu, Xin

AU - Zuo, Kang

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N2 - Let f: S → B be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus g ≥ 2 with relative irregularity qf. We show a sharp lower bound on the slope λf of f. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of λf as an increasing function of qf in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if λf < 4.

AB - Let f: S → B be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus g ≥ 2 with relative irregularity qf. We show a sharp lower bound on the slope λf of f. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of λf as an increasing function of qf in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if λf < 4.

KW - Fibrations

KW - Relative irregularity

KW - Slope inequality

UR - https://www.scopus.com/pages/publications/84995801549

U2 - 10.1090/tran6682

DO - 10.1090/tran6682

M3 - 文章

AN - SCOPUS:84995801549

SN - 0002-9947

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

ER -

On the slope of hyperelliptic fibrations with positive relative irregularity

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Keywords

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