Journal of East China Normal University(Natural Science) >

2021 , Vol. 2021 >Issue 6: 58 - 64

DOI: https://doi.org/10.3969/j.issn.1000-5641.2021.06.007

Mathematics

Singularity indices of hyperelliptic fibrations

  • Zhiming GUO
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  • School of Mathematical Sciences, Soochow University, Suzhou Jiangsu　215006, China

Received date: 2020-09-17

  Online published: 2021-11-26

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Abstract

Xiao introduced a series of singularity indices to survey hyperelliptic fibrations. However, it remains unknown whether the second singularity index, $ s_2 $ , is non-negative. In this paper, I demonstrate a series of examples of degeneration of curves where $s_2$ tends to $-\infty$ as the genus $g$ grows. Moreover, I obtain a lower bound for $s_2$ for a given genus $g$ , thereby confirming that the index $s_2$ of fibrations for genus $g=2,3,4$ is non-negative.

Key words： algebraic surfaces; hyperelliptic fibrations; singularity indices

Cite this article

Zhiming GUO . Singularity indices of hyperelliptic fibrations[J]. Journal of East China Normal University(Natural Science), 2021 , 2021(6) : 58 -64 . DOI: 10.3969/j.issn.1000-5641.2021.06.007

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