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Uspekhi Mat. Nauk, 1978, Volume 33, Issue 5(203), Pages 77–89 (Mi umn3519)  

This article is cited in 47 scientific papers (total in 48 papers)

Complex topological characteristics of real algebraic curves

V. A. Rokhlin


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English version:
Russian Mathematical Surveys, 1978, 33:5, 85–98

Bibliographic databases:

UDC: 513.83
MSC: 14P25, 14H50, 14H20
Received: 09.01.1978

Citation: V. A. Rokhlin, “Complex topological characteristics of real algebraic curves”, Uspekhi Mat. Nauk, 33:5(203) (1978), 77–89; Russian Math. Surveys, 33:5 (1978), 85–98

Citation in format AMSBIB
\Bibitem{Rok78}
\by V.~A.~Rokhlin
\paper Complex topological characteristics of~real algebraic curves
\jour Uspekhi Mat. Nauk
\yr 1978
\vol 33
\issue 5(203)
\pages 77--89
\mathnet{http://mi.mathnet.ru/umn3519}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=511882}
\zmath{https://zbmath.org/?q=an:0437.14013|0444.14018}
\transl
\jour Russian Math. Surveys
\yr 1978
\vol 33
\issue 5
\pages 85--98
\crossref{https://doi.org/10.1070/RM1978v033n05ABEH002514}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Zvonilov, “Refinement of the Petrovskii–Arnol'd inequality for curves of odd degree”, Funct. Anal. Appl., 13:4 (1979), 262–268  mathnet  crossref  mathscinet  zmath
    2. V. A. Rokhlin, “New inequalities in the topology of real planar algebraic curves”, Funct. Anal. Appl., 14:1 (1980), 29–33  mathnet  crossref  mathscinet  zmath
    3. V. M. Kharlamov, “Rigid isotopic classification of real planar curves of degree 5”, Funct. Anal. Appl., 15:1 (1981), 73–74  mathnet  crossref  mathscinet  zmath  isi
    4. T. Fidler, “Pencils of lines and the topology of real algebraic curves”, Math. USSR-Izv., 21:1 (1983), 161–170  mathnet  crossref  mathscinet  zmath
    5. V. I. Zvonilov, “Complex topological characteristics of real algebraic curves on surfaces”, Funct. Anal. Appl., 16:3 (1982), 202–204  mathnet  crossref  mathscinet  zmath  isi
    6. V. V. Nikulin, “Involutions of integral quadratic forms and their applications to real algebraic geometry”, Math. USSR-Izv., 22:1 (1984), 99–172  mathnet  crossref  mathscinet  zmath
    7. 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
    8. V. M. Kharlamov, “Classification of nonsingular surfaces of degree $4$ in $\mathbb{RP}^3$ with respect to rigid isotopies”, Funct. Anal. Appl., 18:1 (1984), 39–45  mathnet  crossref  mathscinet  zmath  isi
    9. T. Fidler, “Additional inequalities in the topology of real plane algebraic curves”, Math. USSR-Izv., 27:1 (1986), 183–191  mathnet  crossref  mathscinet  zmath
    10. E. I. Shustin, “Counterexamples to a conjecture of Rokhlin”, Funct. Anal. Appl., 19:2 (1985), 162–163  mathnet  crossref  mathscinet  zmath  isi
    11. 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
    12. V. I. Arnol'd, A. M. Vershik, O. Ya. Viro, A. N. Kolmogorov, S. P. Novikov, Ya. G. Sinai, D. B. Fuchs, “Vladimir Abramovich Rokhlin (obituary)”, Russian Math. Surveys, 41:3 (1986), 189–195  mathnet  crossref  mathscinet  zmath  isi
    13. G. M. Polotovsky, “Connection between the rigid isotopy class of a fifth-order nonsingular curve in $\mathbb{R}P^2$ and its disposition with respect to a line”, Funct. Anal. Appl., 20:4 (1986), 330–332  mathnet  crossref  mathscinet  zmath  isi
    14. 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
    15. 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
    16. 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
    17. A. I. Degtyarev, V. I. Zvonilov, “Rigid isotopy classification of real algebraic curves of bidegree $(3,3)$ on quadrics”, Math. Notes, 66:6 (1999), 670–674  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. 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
    19. 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
    20. Jibin Li, H. S. Y. Chan, K. W. Chung, “Some lower bounds forH(n) in Hilbert’s 16th problem”, Qual Th Dyn Syst, 3:2 (2002), 345  crossref  mathscinet  zmath
    21. Welschinger, JY, “Real algebraic curves and flexible curves on regulated surfaces of base CP1”, Proceedings of the London Mathematical Society, 85 (2002), 367  crossref  mathscinet  zmath  isi
    22. Touze, SFL, “A flexible affine M-sextic which is algebraically unrealizable”, Journal of Algebraic Geometry, 11:2 (2002), 293  mathscinet  zmath  isi
    23. Ilia Itenberg, Eugenii Shustin, “Viro theorem and topology of real and complex combinatorial hypersurfaces”, Isr J Math, 133:1 (2003), 189  crossref  mathscinet  zmath  isi  elib
    24. S. Yu. Orevkov, E. I. Shustin, “Pseudoholomorphic algebraically unrealizable curves”, Mosc. Math. J., 3:3 (2003), 1053–1083  mathnet  mathscinet  zmath
    25. Korchagin, AB, “On arrangements of a plane real quintic curve with respect to a pair of lines”, Communications in Contemporary Mathematics, 5:1 (2003), 1  crossref  mathscinet  zmath  isi  elib
    26. JIBIN LI, “HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS”, Int. J. Bifurcation Chaos, 13:01 (2003), 47  crossref
    27. V. A. Krasnov, “Rigid isotopy classification of real three-dimensional cubics”, Izv. Math., 70:4 (2006), 731–768  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    28. O. Ya. Viro, “Whitney number of closed real algebraic affine curve of type I”, Mosc. Math. J., 6:1 (2006), 211–217  mathnet  mathscinet  zmath
    29. V. A. Krasnov, “The topological classification of Fano surfaces of real three-dimensional cubics”, Izv. Math., 71:5 (2007), 863–894  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    30. Gilmer, PM, “ARF invariants of real algebraic curves”, Pacific Journal of Mathematics, 230:2 (2007), 297  crossref  mathscinet  zmath  isi
    31. V. V. Kozlov, “Topology of Real Algebraic Curves”, Funct. Anal. Appl., 42:2 (2008), 98–102  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    32. V. A. Krasnov, “Equivariant Topological Classification of the Fano Varieties of Real Four-Dimensional Cubics”, Math. Notes, 85:4 (2009), 574–583  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    33. V. A. Krasnov, “On the Fano Variety of a Class of Real Four-Dimensional Cubics”, Math. Notes, 85:5 (2009), 682–689  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    34. V. A. Krasnov, “Topological Classification of Real Three-Dimensional Cubics”, Math. Notes, 85:6 (2009), 841–847  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    35. Fiedler-Le Touze, S, “M-curves of degree 9 with deep nests”, Journal of the London Mathematical Society-Second Series, 79 (2009), 649  mathscinet  zmath  isi
    36. V. A. Krasnov, “Real three-dimensional biquadrics”, Izv. Math., 74:4 (2010), 781–804  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    37. Alexander Nabutovsky, “Non-recursive functions, knots “with thick ropes,” and self-clenching “thick” hyperspheres”, Comm Pure Appl Math, 48:4 (2010), 381  crossref
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    39. Finashin S., Kharlamov V., “Topology of real cubic fourfolds”, Journal of Topology, 3:1 (2010), 1–28  crossref  isi
    40. V. A. Krasnov, “Real four-dimensional biquadrics”, Izv. Math., 75:2 (2011), 371–394  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    41. V. A. Krasnov, “Rigid Isotopy Classification of Real Quadric Line Complexes and Associated Kummer Surfaces”, Math. Notes, 89:5 (2011), 661–671  mathnet  crossref  crossref  mathscinet  isi
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    44. V. A. Krasnov, “Cohomology of real three-dimensional triquadrics”, Izv. Math., 76:1 (2012), 113–138  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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    46. G. M. Polotovskii, “V. V. Morozov, D. A. Gudkov i pervaya chast $16$-i problemy Gilberta”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 31–43  mathnet
    47. V. A. Krasnov, “Real $M$-triquadrics”, Izv. Math., 77:1 (2013), 30–43  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    48. V. A. Krasnov, “On a classical correspondence of real K3 surfaces”, Izv. Math., 82:4 (2018), 662–693  mathnet  crossref  crossref  adsnasa  isi  elib
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