A Lower Bound on the Euler–Poincaré Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves. (1st February 2016)

• Record Type: Journal Article
• Authors: Ishida, Hirotaka
• Is Part Of: Canadian journal of mathematics. Volume 68:Number 1(2016)
• Page Start: 67
• Page End: 87
• Publication Date: 2016-02-01
• Subjects: 14D05 -- 14J29 -- 14H30; hyperelliptic fibration -- surface of general type -- double cover; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2015-032-8
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: 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.