On the Geography of Slopes of Fibrations

Xiao Lei Liu; Jun Lu

doi:10.4171/prims/60-4-3

On the Geography of Slopes of Fibrations

Xiao Lei Liu
, Jun Lu

School of Mathematical Sciences

Dalian University of Technology

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

Abstract

The slopes of fibrations of genus g ≥ 2 have strict lower (resp., upper) bound, namely λ_m(g) (resp., λ_M (g)). In this paper, we show that if g ≠ 3, then each rational number r ∈ [λ_m(g), λ_M (g)] can occur as the slope of some fibration of genus g. A similar result is also true for g = 3 and r ∈ [λ_m(3), 9].

Original language	English
Pages (from-to)	723-739
Number of pages	17
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	60
Issue number	4
DOIs	https://doi.org/10.4171/prims/60-4-3
State	Published - 2024

Keywords

Chern number
Kodaira fibration
base change
cyclic cover
modular invariant
singular fiber
slope

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title = "On the Geography of Slopes of Fibrations",

abstract = "The slopes of fibrations of genus g ≥ 2 have strict lower (resp., upper) bound, namely λm(g) (resp., λM (g)). In this paper, we show that if g ≠ 3, then each rational number r ∈ [λm(g), λM (g)] can occur as the slope of some fibration of genus g. A similar result is also true for g = 3 and r ∈ [λm(3), 9].",

keywords = "Chern number, Kodaira fibration, base change, cyclic cover, modular invariant, singular fiber, slope",

author = "Liu, \{Xiao Lei\} and Jun Lu",

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doi = "10.4171/prims/60-4-3",

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T1 - On the Geography of Slopes of Fibrations

AU - Liu, Xiao Lei

AU - Lu, Jun

PY - 2024

Y1 - 2024

N2 - The slopes of fibrations of genus g ≥ 2 have strict lower (resp., upper) bound, namely λm(g) (resp., λM (g)). In this paper, we show that if g ≠ 3, then each rational number r ∈ [λm(g), λM (g)] can occur as the slope of some fibration of genus g. A similar result is also true for g = 3 and r ∈ [λm(3), 9].

AB - The slopes of fibrations of genus g ≥ 2 have strict lower (resp., upper) bound, namely λm(g) (resp., λM (g)). In this paper, we show that if g ≠ 3, then each rational number r ∈ [λm(g), λM (g)] can occur as the slope of some fibration of genus g. A similar result is also true for g = 3 and r ∈ [λm(3), 9].

KW - Chern number

KW - Kodaira fibration

KW - base change

KW - cyclic cover

KW - modular invariant

KW - singular fiber

KW - slope

UR - https://www.scopus.com/pages/publications/85209914882

U2 - 10.4171/prims/60-4-3

DO - 10.4171/prims/60-4-3

M3 - 文章

AN - SCOPUS:85209914882

SN - 0034-5318

VL - 60

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EP - 739

JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

IS - 4

ER -

On the Geography of Slopes of Fibrations

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Keywords

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