Recovery of Plane Curves from Branch Points
Algebraic Geometry
2023-04-14 v2 Computational Geometry
Abstract
We recover plane curves from their branch points under projection onto a line. Our focus lies on cubics and quartics. These have 6 and 12 branch points respectively. The plane Hurwitz numbers 40 and 120 count the orbits of solutions. We determine the numbers of real solutions, and we present exact algorithms for recovery. Our approach relies on 150 years of beautiful algebraic geometry, from Clebsch to Vakil and beyond.
Keywords
Cite
@article{arxiv.2205.11287,
title = {Recovery of Plane Curves from Branch Points},
author = {Daniele Agostini and Hannah Markwig and Clemens Nollau and Victoria Schleis and Javier Sendra-Arranz and Bernd Sturmfels},
journal= {arXiv preprint arXiv:2205.11287},
year = {2023}
}
Comments
Section 5 has been revised and expanded. 20 pages