Hirzebruch曲面上的三角Morsifications（附E.舒斯廷
Trigonal Morsifications on Hirzebruch Surfaces with an appendix by E. Shustin
摘要：
本文给出了Hirzebruch曲面$Σ_n$上具有最大数目的非退化二重点的全可约三角曲线的刚性合痕类的分类.这样的曲线对应于权重为$(3,3n)$的全实半拟齐次奇异性的morsification（三个光滑实分支的并集，它们以重数$n$相交）。我们通过研究dessins的组合性质得到了这个分类。在附录中，我们证明了权为$(3,3n)$的全实半拟齐次奇点的任何Morsification都可以通过将方程限制在牛顿图上并在牛顿图下添加单项式来实现（直到合痕）。
英文摘要：
In this paper we obtain a classification of rigid isotopy classes of totally reducible trigonal curves lying on a Hirzebruch surface $Σ_n$, and having a maximal number of non-degenerated double points. Such curves correspond to morsifications of a totally real semiquasihomogeneous singularity of weight $(3,3n)$ (the union of three smooth real branches intersecting each other with multiplicity $n$). We obtain this classification by studying combinatorial properties of dessins. In the appendix, we prove that any morsification of a totally real semiquasihomogeneous singularity of weight $(3,3n)$ can be realized (up to isotopy) by the restriction of the equation to the Newton diagram and adding monomials under the Newton diagram.
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