Abstract
For each integer g ⩾ 2, we construct a family of hyperelliptic curves of genus g whose slope reaches the upper bound obtained by Xiao.
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Lu J, Tan S L. Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves. Trans Amer Math Soc, 2013, 365: 3373–3396
Tan S L. On the base changes of pencils of curves, I. Manuscripta Math, 1994, 84: 225–244
Tan S L. On the base changes of pencils of curves, II. Math Z, 1996, 222: 655–676
Tan S L. Chern numbers of a singular fiber, modular invariants and isotrivial families of curves. Acta Math Vietnam, 2010, 35: 159–172
Tan S L, Tu Y, Zamora A G. On complex surfaces with 5 or 6 semistable singular fibers over ℙ1. Math Z, 1996, 249: 427–438
Xiao G. Surfaces fibrées en courbes de genre deux. Lecture Notes in Mathematics, vol. 1137. New York: Springer-Verlag, 1985
Xiao G. The Fibrations of Algbraic Surfaces (in Chinese). Shanghai: Shanghai Scientific & Technical Publishers, 1992
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Liu, X., Tan, S. Families of hyperelliptic curves with maximal slopes. Sci. China Math. 56, 1743–1750 (2013). https://doi.org/10.1007/s11425-013-4634-9
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DOI: https://doi.org/10.1007/s11425-013-4634-9