PreprintCC BY-NC-SA 4.0HAL
Non-existence of separating morphisms of low degree
Abstract
A separating curve is a real curve whose real part disconnects its complex part. It also admits totally real morphisms to the projective line, and the separating gonality is the minimal possible degree for such morphisms. The separating gonality is bounded from below by the number of connected components of the real part of the curve. In this paper, we build on a strategy of Manzaroli to improve this lower bound for some curves embedded in the projective plane or in a Hirzebruch surface.
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BibTeX
@misc{demory2026nonexistence,
title = {{Non-existence of separating morphisms of low degree}},
author = {Aloïs Demory and Gurvan Mével and Antoine Toussaint},
howpublished = {HAL},
year = {2026},
month = aug,
eprint = {2608.26927},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05730172v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Non-existence of separating morphisms of low degree
AU - Aloïs Demory
AU - Gurvan Mével
AU - Antoine Toussaint
PY - 2026
DA - 2026/08/27
PB - HAL
UR - https://hal.science/hal-05730172v1
AB - A separating curve is a real curve whose real part disconnects its complex part. It also admits totally real morphisms to the projective line, and the separating gonality is the minimal possible degree for such morphisms. The separating gonality is bounded from below by the number of connected components of the real part of the curve. In this paper, we build on a strategy of Manzaroli to improve this lower bound for some curves embedded in the projective plane or in a Hirzebruch surface.
ER -