Year: 2025
Type: article
Abstract: 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 separating . The degree of such f is bounded from below by the number l of real connected components of 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 k d ≤ l .
DOI: 10.5802/afst.1798
Author: Matilde Manzaroli
Institution: University of Tübingen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409765496