关于亏格g超椭圆纤维化的奇异纤维的一些组合条件

Some Combinatorial Conditions on the Singular Fibre of a Hyperelliptic Fibration of Genus g

对于一个相对极小的亏格g≥2超椭圆纤维化的奇异纤维，引进了分类对偶图的概念．利用二次复盖和曲线上的Riemann－Hurwitz公式，得到了两个组合条件．利用这两条性质，可判定某些带有给定奇异纤维的超椭圆纤维化是不存在的．

For the Singular fibre of a relatively minimal hyperelliptic fibration of genus g≥2,we introduce the concept of class dual graph.Using the double cover and Riemann-Hurwitz formula, we obtain two combinatorial conditions. We can use the two properties as above to showthat there are no hyperelliptic fibration with given singular fibre.