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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
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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 hyperelliptic fibration, surface of general type, double cover
MSC Classifications: 14D05, 14J29, 14H30 show english descriptions Structure of families (Picard-Lefschetz, monodromy, etc.)
Surfaces of general type
Coverings, fundamental group [See also 14E20, 14F35]
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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