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October, 2020 The number of singular fibers in hyperelliptic Lefschetz fibrations
Tülin ALTUNÖZ
J. Math. Soc. Japan 72(4): 1309-1325 (October, 2020). DOI: 10.2969/jmsj/82988298

Abstract

We consider complex surfaces, viewed as smooth 4-dimensional manifolds, that admit hyperelliptic Lefschetz fibrations over the 2-sphere. In this paper, we show that the minimal number of singular fibers of such fibrations is equal to $2g+4$ for even $g\geq4$. For odd $g\geq7$, we show that the number is greater than or equal to $2g+6$. Moreover, we discuss the minimal number of singular fibers in all hyperelliptic Lefschetz fibrations over the 2-sphere as well.

Funding Statement

The author was partially supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK).

Citation

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Tülin ALTUNÖZ. "The number of singular fibers in hyperelliptic Lefschetz fibrations." J. Math. Soc. Japan 72 (4) 1309 - 1325, October, 2020. https://doi.org/10.2969/jmsj/82988298

Information

Received: 8 July 2019; Published: October, 2020
First available in Project Euclid: 17 August 2020

MathSciNet: MR4165934
Digital Object Identifier: 10.2969/jmsj/82988298

Subjects:
Primary: 57M99
Secondary: 20F38

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 4 • October, 2020
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