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A Lower Bound on the Euler–Poincaré Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves

Published online by Cambridge University Press:  20 November 2018

Hirotaka Ishida
Hirotaka Ishida*
Affiliation:
General Education, Ube National College of Technology, Tokiwadai, Ube 755-8555, Japan e-mail: ishida@ube-k.ac.jp
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Abstract

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Let $S$ be a surface of general type. In this article, when there exists a relatively minimal hyperelliptic fibration $f:\,S\,\to \,{{\mathbb{P}}^{1}}$ whose slope is less than or equal to four, we give a lower bound on the Euler–Poincaré characteristic of $S$. Furthermore, we prove that our bound is the best possible by giving required hyperelliptic fibrations.

Keywords

14D0514J2914H30hyperelliptic fibrationsurface of general typedouble cover
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 1 , 01 February 2016 , pp. 67 - 87
Copyright
Copyright © Canadian Mathematical Society 2016

References

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