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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:2015-10-21
Printed: Feb 2016
• Hirotaka Ishida,
General Education, Ube National College of Technology, Tokiwadai, Ube 755-8555, Japan
 Format: LaTeX MathJax PDF

## Abstract

Let $S$ be a surface of general type. In this article, when there exists a relatively minimal hyperelliptic fibration $f \colon S \rightarrow \mathbb{P}^1$ whose slope is less than or equal to four, we show the 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: hyperelliptic fibration, surface of general type, double cover
 MSC Classifications: 14D05 - Structure of families (Picard-Lefschetz, monodromy, etc.) 14J29 - Surfaces of general type 14H30 - Coverings, fundamental group [See also 14E20, 14F35]

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