This article is cited in 12 scientific papers (total in 12 papers)
Pencils of lines and the topology of real algebraic curves
Using a pencil of lines, a new restriction on the location of ovals of a nonsingular plane curve is obtained. It turns out that the location of a curve separating its complexification with respect to a pencil of lines determines to a significant degree the complex orientation of the curve. Furthermore, a new invariant of the strict isotopy type of the curve is given, which in particular distinguishes some seventh degree $M$-curves with the same complex scheme. A restriction on the complex orientation of seventh degree $M$-curves is proved.
Bibliography: 9 titles.
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Mathematics of the USSR-Izvestiya, 1983, 21:1, 161–170
MSC: 14H45, 14N05
T. Fidler, “Pencils of lines and the topology of real algebraic curves”, Izv. Akad. Nauk SSSR Ser. Mat., 46:4 (1982), 853–863; Math. USSR-Izv., 21:1 (1983), 161–170
Citation in format AMSBIB
\paper Pencils of lines and the topology of real algebraic curves
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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A. B. Korchagin, E. I. Shustin, “Affine curves of degree 6 and smoothings of a nondegenerate sixth order singular point”, Math. USSR-Izv., 33:3 (1989), 501–520
E. I. Shustin, “New restrictions on the topology of real curves of degree a multiple of 8”, Math. USSR-Izv., 37:2 (1991), 421–443
S. Yu. Orevkov, “A new affine $M$-sextic. II”, Russian Math. Surveys, 53:5 (1998), 1099–1101
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A. I. Degtyarev, V. M. Kharlamov, “Topological properties of real algebraic varieties: du coté de chez Rokhlin”, Russian Math. Surveys, 55:4 (2000), 735–814
S. Yu. Orevkov, “Link Theory and New Restrictions for $M$-Curves of Degree Nine”, Funct. Anal. Appl., 34:3 (2000), 229–231
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STEPAN YU. OREVKOV, “PLANE REAL ALGEBRAIC CURVES OF ODD DEGREE WITH A DEEP NEST”, J. Knot Theory Ramifications, 14:04 (2005), 497
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