完全真实的三次铅笔相对于六次铅笔
Totally real pencils of cubics with respect to sextics
摘要：
一条实代数平面曲线$A$被称为是可除的，如果它的实部$\mathbb{R}A$不连接它的复部$\mathbb{C}A$。曲线束关于$A$是全实的，如果它与$\mathbb{C}A$只有实交点。如果存在这样一个笔，那么$A$正在划分，这是$M$ -曲线的情况。反过来说，任何分界曲线都能被赋予一根完全真实的铅笔吗？我们在这里研究的情况下，$M-2$ -六次曲线有2个或6个空的外部椭圆。这样的性别总是分裂的。我们证明，他们实际上可能被赋予一个完全真实的铅笔的立方。
英文摘要：
A real algebraic plane curve $A$ is said to be dividing if its real part $\mathbb{R}A$ disconnects its complex part $\mathbb{C}A$. A pencil of curves is totally real with respect to $A$ if it has only real intersections with $\mathbb{C}A$. If there exists such a pencil, then $A$ is dividing, this is the case for the $M$-curves. Can conversely any dividing curve be endowed with a totally real pencil? We study here the case of $M-2$-sextics having 2 or 6 empty exterior ovals. Such sextics are always dividing. We prove that they may actually be endowed with a totally real pencil of cubics.
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