Recovery of Plane Curves from Branch Points-Reference-Cited by-同舟云学术

Recovery of Plane Curves from Branch Points

Published:2023-09-07 Issue: Volume: Page:
ISSN:0179-5376
Container-title:Discrete & Computational Geometry
language:en
Short-container-title:Discrete Comput Geom

Author:

Agostini Daniele,Markwig Hannah,Nollau Clemens,Schleis Victoria,Sendra-Arranz Javier,Sturmfels Bernd

Abstract

AbstractWe 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.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science

Link

https://link.springer.com/content/pdf/10.1007/s00454-023-00538-5.pdf

Reference30 articles.

1. Breiding, P., Rose, K., Timme, S.: Certifying zeros of polynomial systems using interval arithmetic. ACM Trans. Math. Softw. 49(1), $$\#\,$$11 (2023)

2. Breiding, P., Timme, S.: HomotopyContinuation.jl: a package for homotopy continuation in Julia. In: 6th International Conference on Mathematical Software (South Bend 2018). Lecture Notes in Computer Science, vol. 10931, pp. 458–465. Springer, New York (2018)

3. Cadoret, A.: Counting real Galois covers of the projective line. Pac. J. Math. 219(1), 53–81 (2005)

4. Cavalieri, R., Johnson, P., Markwig, H.: Tropical Hurwitz numbers. J. Algebraic Comb. 32(2), 241–265 (2010)

5. Cavalieri, R., Miles, E.: Riemann Surfaces and Algebraic Curves: A First Course in Hurwitz Theory. London Mathematical Society Student Texts, vol. 87. Cambridge University Press, Cambridge (2016)