The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations

Tulin Altunoz

doi:10.2969/jmsj/82988298

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arXiv · 2004.09093

The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations

Tulin Altunoz

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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.

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BibTeX RIS

Tulin Altunoz. 2020-04-20. The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations. https://doi.org/10.2969/jmsj%2F82988298

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