Geodesic
A Lower Bound on the Euler–Poincaré Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves
Canadian journal of mathematics, Tome 68 (2016) no. 1, pp. 67-87

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DOI

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.
DOI : 10.4153/CJM-2015-032-8
Mots-clés : 14D05, 14J29, 14H30, hyperelliptic fibration, surface of general type, double cover 
Ishida, Hirotaka. A Lower Bound on the Euler–Poincaré Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves. Canadian journal of mathematics, Tome 68 (2016) no. 1, pp. 67-87. doi: 10.4153/CJM-2015-032-8
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     title = {A {Lower} {Bound} on the {Euler{\textendash}Poincar\'e} {Characteristic} of {Certain} {Surfaces} of {General} {Type} with a {Linear} {Pencil} of {Hyperelliptic} {Curves}},
     journal = {Canadian journal of mathematics},
     pages = {67--87},
     year = {2016},
     volume = {68},
     number = {1},
     doi = {10.4153/CJM-2015-032-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-032-8/}
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