Graphs of trigonal curves and rigid isotopies of singular real algebraic curves of bidegree (4, 3) on a hyperboloid
https://doi.org/10.26907/2949-3919.2025.1.26-51
Abstract
A rigid isotopy of real algebraic curves of a certain class is a path in the space of curves of this class. Our study completes the rigid isotopic classification of nonsingular real algebraic curves of bidegree (4,3) on a hyperboloid, started by the author in his earlier works. Missing proofs of the uniqueness of the connected components for 16 classes of real algebraic curves of bidegree (4,3) having a single node or a cusp are given. The main technical tools are graphs of real trigonal curves on Hirzebruch surfaces.
Supporting agencies: The work was completed within the framework of a scientific project of the State assignment FSWR-2023-0034
About the Author
V. I. Zvonilov
Lobachevsky State University of Nizhny Novgorod
Russian Federation
Russian Federation
Victor Ivanovich Zvonilov
23 Gagarin av., Nizhny Novgorod, 603950
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Review
For citations:
Zvonilov V.I. Graphs of trigonal curves and rigid isotopies of singular real algebraic curves of bidegree (4, 3) on a hyperboloid. Mathematics and Theoretical Computer Science. 2025;3(1):26-51. (In Russ.) https://doi.org/10.26907/2949-3919.2025.1.26-51
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