超椭圆Lefschetz纤维中奇异纤维的数量

arXiv: Geometric Topology Pub Date : 2020-04-01 DOI:10.2969/JMSJ/82988298

Tulin Altunoz

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引用次数: 2

摘要

我们考虑复杂曲面，将其视为光滑的$4$维流形，它在$2$ -球面上允许超椭圆的Lefschetz振动。在本文中，我们证明了这种纤维的最小奇异纤维数等于$2g+4$对于偶数$g\geq4$。对于奇数$g\geq7$，我们证明该数大于等于$2g+6$。此外，我们还讨论了$2$ -球上所有超椭圆Lefschetz纤振中奇异纤维的最小数量。

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The number of singular fibers in hyperelliptic Lefschetz fibrations

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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arXiv: Geometric Topology

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