论文标题
存在分离形态和完全真实铅笔的障碍物
Obstructions for the existence of separating morphisms and totally real pencils
论文作者
论文摘要
可以追溯到AHLFORS，一个真正的代数曲线$ c $在且仅当曲线的真实部分断开其复杂部分时，即曲线为\ textit {sapeating}时，就会将形态$ f $与复杂的投影线分开。此类$ f $的程度从下面的数字$ l $限制在$ \ mathbb {r} c $的实际连接组件的数字$ l $。这种界限的清晰度并不是先验的。我们证明，真正的代数分离曲线，嵌入在某些环境表面，并以某种方式界定$ l $，不承认分离可能程度最低的形态。此外，这种不存在的结果可以应用于某些实际分离平面曲线$ d $，不要承认完全是$ k $的曲线的真实铅笔，这样$ kd \ leq l $。
It goes back to Ahlfors that a real algebraic curve $C$ admits a separating morphism $f$ to the complex projective line if and only if the real part of the curve disconnects its complex part, i.e. the curve is \textit{separating}. The degree of such $f$ is bounded from below by the number $l$ of real connected components of $ \mathbb{R} C$. The sharpness of this bound is not a priori clear. We prove that real algebraic separating curves, embedded in some ambient surface and with $l$ bounded in a certain way, do not admit separating morphisms of lowest possible degree. Moreover, this result of non-existence can be applied to show that certain real separating plane curves of degree $d$, do not admit totally real pencils of curves of degree $k$ such that $kd \leq l$.
