论文标题
过度纤维化Lefschetz纤维中的奇异纤维数量
The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations
论文作者
论文摘要
我们认为复杂的表面被认为是光滑的$ 4 $维歧管，可以在$ 2 $ -sphere上允许过度纤维化的Lefschetz纤维纤维。在本文中，我们表明，这种纤维的奇异纤维数量最少等于$ g \ geq4 $的$ 2G+4 $。对于奇数$ g \ geq7 $，我们表明该数字大于或等于$ 2G+6 $。此外，我们在$ 2 $ -SPHERE上也讨论了所有过ellip纤维纤维中的奇异纤维数量最少。
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.
