Uniform bound for the effective Bogomolov conjecture

Liu, Xiao-Lei; Tan, Sheng-Li

doi:10.1016/j.crma.2017.01.003

Cited by 3 publications

(3 citation statements)

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“…Though we have given a uniform lower bound of the effective Bogomolov conjecture for general g, see [LT17]. We now give a better bound for g = 2, 3.…”

Section: Effective Bogomolov Conjecturementioning

confidence: 80%

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Fractional Dehn twists and modular invariants

Liu

2020

Sci. China Math.

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In this paper, we aim to give explicit lower bounds of modular invariants of families of curves of genus 2 and 3. According to the relation between fractional Dehn twists and modular invariants, we give the sharp lower bounds of fractional Dehn twist coefficients and classify pseudo-periodic maps with minimal coefficients firstly. Then we give explicit lower bounds of modular invariants, which are sharp for genus 2. We also obtain equivalent conditions for families of curves with these bounds. As an application, we give a better uniform lower bounds for the effective Bogomolov conjecture for genus 2 and 3.

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“…Though we have given a uniform lower bound of the effective Bogomolov conjecture for general g, see [LT17]. We now give a better bound for g = 2, 3.…”

Section: Effective Bogomolov Conjecturementioning

confidence: 80%

“…Remark that the bounds given in [LT17] are 1 12160 for g = 2 and 1 19656 for g = 3. The organization of this paper is as follows.…”

Section: Effective Bogomolov Conjecturementioning

confidence: 98%

Fractional Dehn twists and modular invariants

Liu

2020

Sci. China Math.

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“…Modular invariants are basic in the study of fibrations of algebraic surfaces and moduli spaces of algebraic curves, see [Ta10,LT13,Li16,No07]. In arithmetic algebraic geometry, modular invariants are some heights of algebraic curves, and can be used to give uniformity properties of curves, see [LT17].…”

Section: Introductionmentioning

confidence: 99%

Fractional Dehn twists and modular invariants

Liu

2019

Preprint

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On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients

Tan

2022

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Modular invariants of families of curves are Arakelov invariants in arithmetic algebraic geometry. All the known uniform lower bounds of these invariants are not sharp. In this paper, we aim to give explicit lower bounds of modular invariants of families of curves, which is sharp for genus 2. According to the relation between fractional Dehn twists and modular invariants, we give the sharp lower bounds of fractional Dehn twist coefficients and classify pseudo-periodic maps with minimal coefficients for genus 2 and 3 firstly. We also obtain a rigidity property for families with minimal modular invariants, and other applications.

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Uniform bound for the effective Bogomolov conjecture

Cited by 3 publications

References 13 publications

Fractional Dehn twists and modular invariants

Fractional Dehn twists and modular invariants

Fractional Dehn twists and modular invariants

On the sharp lower bounds of modular invariants and fractional Dehn twist coefficients

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