Journal of East China Normal University(Natural Science) ›› 2021, Vol. 2021 ›› Issue (6): 58-64.doi: 10.3969/j.issn.1000-5641.2021.06.007

• Mathematics • Previous Articles     Next Articles

Singularity indices of hyperelliptic fibrations

Zhiming GUO()   

  1. School of Mathematical Sciences, Soochow University, Suzhou Jiangsu 215006, China
  • Received:2020-09-17 Online:2021-11-25 Published:2021-11-26


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

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