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Recovery of Plane Curves from Branch Points.

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Title: Recovery of Plane Curves from Branch Points.
Authors: Agostini, Daniele1 (AUTHOR), Markwig, Hannah1 (AUTHOR), Nollau, Clemens1 (AUTHOR), Schleis, Victoria1 (AUTHOR), Sendra-Arranz, Javier2 (AUTHOR), Sturmfels, Bernd2,3 (AUTHOR) bernd@mis.mpg.de
Source: Discrete & Computational Geometry. Sep2024, Vol. 72 Issue 2, p451-475. 25p.
Subjects: Algebraic geometry, Hurwitz polynomials, Number systems, Orbits (Astronomy), Algorithms
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. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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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. [ABSTRACT FROM AUTHOR]
ISSN:01795376
DOI:10.1007/s00454-023-00538-5