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

This article is cited in 12 scientific papers (total in 12 papers)

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
Received: 25.11.1980

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
\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
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 1
\pages 161--170

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    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  mathnet  crossref  mathscinet  zmath
    2. T. Fidler, “Additional inequalities in the topology of real plane algebraic curves”, Math. USSR-Izv., 27:1 (1986), 183–191  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath  adsnasa
    6. S. Yu. Orevkov, “A new affine $M$-sextic. II”, Russian Math. Surveys, 53:5 (1998), 1099–1101  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. S. Yu. Orevkov, “Link Theory and New Restrictions for $M$-Curves of Degree Nine”, Funct. Anal. Appl., 34:3 (2000), 229–231  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. S. Yu. Orevkov, E. I. Shustin, “Flexible, algebraically unrealizable curves: rehabilitation of Hilbert-Rohn-Gudkov approach”, crll, 2002:551 (2002), 145  crossref  mathscinet  zmath  elib
    11. STEPAN YU. OREVKOV, “PLANE REAL ALGEBRAIC CURVES OF ODD DEGREE WITH A DEEP NEST”, J. Knot Theory Ramifications, 14:04 (2005), 497  crossref
    12. O. Ya. Viro, “Whitney number of closed real algebraic affine curve of type I”, Mosc. Math. J., 6:1 (2006), 211–217  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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