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 Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 4, Pages 853–863 (Mi izv1649)

Pencils of lines and the topology of real algebraic curves

T. Fidler

Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1983, 21:1, 161–170

Bibliographic databases:

UDC: 513.6
MSC: 14H45, 14N05

Citation: 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
\Bibitem{Fid82} \by T.~Fidler \paper Pencils of lines and the topology of real algebraic curves \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1982 \vol 46 \issue 4 \pages 853--863 \mathnet{http://mi.mathnet.ru/izv1649} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=670168} \zmath{https://zbmath.org/?q=an:0522.14014} \transl \jour Math. USSR-Izv. \yr 1983 \vol 21 \issue 1 \pages 161--170 \crossref{https://doi.org/10.1070/IM1983v021n01ABEH001647} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. O. Ya. Viro, “Real plane curves of degrees 7 and 8: new prohibitions”, Math. USSR-Izv., 23:2 (1984), 409–422
2. T. Fidler, “Additional inequalities in the topology of real plane algebraic curves”, Math. USSR-Izv., 27:1 (1986), 183–191
3. O. Ya. Viro, “Progress in the topology of real algebraic varieties over the last six years”, Russian Math. Surveys, 41:3 (1986), 55–82
4. 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
5. 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
6. S. Yu. Orevkov, “A new affine $M$-sextic. II”, Russian Math. Surveys, 53:5 (1998), 1099–1101
7. S. Yu. Orevkov, “Prospective conics and $M$-quintics in general position with a maximally intersecting pair of ovals”, Math. Notes, 65:4 (1999), 528–532
8. 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
9. S. Yu. Orevkov, “Link Theory and New Restrictions for $M$-Curves of Degree Nine”, Funct. Anal. Appl., 34:3 (2000), 229–231
10. S. Yu. Orevkov, E. I. Shustin, “Flexible, algebraically unrealizable curves: rehabilitation of Hilbert-Rohn-Gudkov approach”, crll, 2002:551 (2002), 145
11. STEPAN YU. OREVKOV, “PLANE REAL ALGEBRAIC CURVES OF ODD DEGREE WITH A DEEP NEST”, J. Knot Theory Ramifications, 14:04 (2005), 497
12. O. Ya. Viro, “Whitney number of closed real algebraic affine curve of type I”, Mosc. Math. J., 6:1 (2006), 211–217
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