Zvonilov, V. I. Isotopies of real trigonal curves on Hirzebruch surfaces. (English. Russian original) Zbl 1027.14030 J. Math. Sci., New York 113, No. 6, 804-809 (2003); translation from Zap. Nauchn. Semin. POMI 267, 133-142 (2000). From the introduction: V. A. Rokhlin [Russ. Math. Surv. 33, 85-98 (1978); translation from Usp. Mat. Nauk 33, No. 5(203), 77-89 (1978; Zbl 0437.14013)] defined rigid isotopy as a path in the space of nonsingular plane real algebraic curves of a given degree. More generally, a rigid isotopy is a path in the space of curves of a given class. At present, the rigid isotopy classification of real algebraic curves is known for nonsingular curves of degree \(m\leq 6\) on \(\mathbb{R}\mathbb{P}^2\), for nonsingular curves of bidegree \((m,1)\), \((m,2)\), and \((3,3)\) on a hyperboloid and an ellipsoid and for some of the simplest classes of singular curves on the same surfaces. Main theorem: A nonsingular real algebraic curve of bidegree \((m,3)\) on the Hirzebruch surface \(\Sigma_1\) is determined up to rigid isotopy by its real scheme and type of complex conjugation. Cited in 1 Document MSC: 14P25 Topology of real algebraic varieties 14H51 Special divisors on curves (gonality, Brill-Noether theory) 14J25 Special surfaces 14H50 Plane and space curves Keywords:real trigonal curves; rigid isotopy; Hirzebruch surface Citations:Zbl 0437.14013 PDFBibTeX XMLCite \textit{V. I. Zvonilov}, J. Math. Sci., New York 113, No. 6, 804--809 (2000; Zbl 1027.14030); translation from Zap. Nauchn. Semin. POMI 267, 133--142 (2000) Full Text: DOI