Families of hyperelliptic curves with maximal slopes

Liu, Xiao-Lei; Tan, Sheng-Li

doi:10.1007/s11425-013-4634-9

Cited by 11 publications

(4 citation statements)

References 4 publications

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“…From the Corollary 2.15 and Theorem 1.1, we know that a family f : S → C of hyperelliptic semistable curves with lowest slope if and only if the image [f ] of f by the moduli map J intersects with Ξ 0 only, and f with highest slope if and only if [f ] intersects with ∆ [g/2] only. See[7] for families with highest slope.…”

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confidence: 99%

Modular invariants and singularity indices of hyperelliptic fibrations

Liu

2016

Chin. Ann. Math. Ser. B

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The modular invariants of a family of semistable curves are the degrees of the corresponding divisors on the image of the moduli map. The singularity indices were introduced by G. Xiao to classify singular fibers of hyperelliptic fibrations and to compute global invariants locally. In the semistable case, we show that the modular invariants corresponding with the boundary classes are just the singularity indices. As an application, we show that the formula of Xiao for relative Chern numbers is the same as that of Cornalba-Harris in the semistable case.

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confidence: 99%

Modular invariants and singularity indices of hyperelliptic fibrations

Liu

2016

Chin. Ann. Math. Ser. B

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“…Remark 4.4. Theorem 4.3 (3) was shown by Xiao in [19] and the upper bound is known to be sharp [15].…”

Section: γ Pmentioning

confidence: 99%

“…Note also that Theorem 0.3 (3) provides a new proof of Xiao's upper bound for hyperelliptic fibrations in [19] referred above. It is shown in [15] that the inequality is optimal for given g.…”

Section: Introductionmentioning

confidence: 99%

Upper bounds on the slope of certain fibered surfaces

Enokizono¹

2016

Preprint

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We establish the slope equality and give an upper bound of the slope for finite cyclic covering fibrations of an elliptic surface including bielliptic fibrations of genus greater than 5. We also give an upper bound of the slope for triple cyclic covering fibrations of a ruled surface and hyperelliptic fibrations, which provides a new proof of Xiao's upper bound.2010 Mathematics Subject Classification. 14D06.

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“…In particular, if f : X → Y is isotrivial, then δ(f ) = 0. 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%