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Uspekhi Mat. Nauk, 1974, Volume 29, Issue 4(178), Pages 3–79 (Mi umn7210)  

This article is cited in 55 scientific papers (total in 57 papers)

The topology of real projective algebraic varieties

D. A. Gudkov


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English version:
Russian Mathematical Surveys, 1974, 29:4, 1–79

Bibliographic databases:

UDC: 513.83
MSC: 14H50, 14Jxx, 53C55
Received: 05.11.1973

Citation: D. A. Gudkov, “The topology of real projective algebraic varieties”, Uspekhi Mat. Nauk, 29:4(178) (1974), 3–79; Russian Math. Surveys, 29:4 (1974), 1–79

Citation in format AMSBIB
\Bibitem{Gud74}
\by D.~A.~Gudkov
\paper The topology of real projective algebraic varieties
\jour Uspekhi Mat. Nauk
\yr 1974
\vol 29
\issue 4(178)
\pages 3--79
\mathnet{http://mi.mathnet.ru/umn7210}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=399085}
\zmath{https://zbmath.org/?q=an:0316.14018}
\transl
\jour Russian Math. Surveys
\yr 1974
\vol 29
\issue 4
\pages 1--79
\crossref{https://doi.org/10.1070/RM1974v029n04ABEH001288}


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    Erratum

    This publication is cited in the following articles:
    1. D. A. Gudkov, “Pismo v redaktsiyu”, UMN, 30:4(184) (1975), 300–300  mathnet  mathscinet
    2. V. A. Krasnov, “A generalized Petrovsky inequality for odd-degree curves”, Funct. Anal. Appl., 10:2 (1976), 116–121  mathnet  crossref  mathscinet  zmath
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    5. V. M. Kharlamov, “Isotopic types of nonsingular surfaces of fourth degree in $\mathbb{RP}^3$”, Funct. Anal. Appl., 12:1 (1978), 68–69  mathnet  crossref  mathscinet  zmath
    6. S. M. Natanzon, “Automorphisms of the Riemann surface of an $M$-curve”, Funct. Anal. Appl., 12:3 (1978), 228–229  mathnet  crossref  mathscinet  zmath
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    9. 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
    10. D. A. Gudkov, “Generalization of a theorem of brusotti for curves on a surface of second order”, Funct. Anal. Appl., 14:1 (1980), 15–18  mathnet  crossref  mathscinet  zmath
    11. T. Fidler, “Pencils of lines and the topology of real algebraic curves”, Math. USSR-Izv., 21:1 (1983), 161–170  mathnet  crossref  mathscinet  zmath
    12. N. V. Ivanov, “Approximation of smooth manifolds by real algebraic sets”, Russian Math. Surveys, 37:1 (1982), 1–59  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. 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
    14. 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
    15. V. A. Krasnov, “Degenerations of real algebraic varieties”, Math. USSR-Izv., 27:1 (1986), 115–140  mathnet  crossref  mathscinet  zmath
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    17. 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
    18. 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
    19. E. I. Shustin, “Versal deformations in the space of planar curves of fixed degree”, Funct. Anal. Appl., 21:1 (1987), 82–84  mathnet  crossref  mathscinet  zmath  isi
    20. 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
    21. Dennis S. Arnon, Scott McCallum, “A polynomial-time algorithm for the topological type of a real algebraic curve”, Journal of Symbolic Computation, 5:1-2 (1988), 213  crossref
    22. Dennis S. Arnon, “A bibliography of quantifier elimination for real closed fields”, Journal of Symbolic Computation, 5:1-2 (1988), 267  crossref
    23. V. N. Karpushkin, “Topology of the zeros of eigenfunctions”, Funct. Anal. Appl., 23:2 (1989), 218–220  mathnet  crossref  mathscinet  zmath  isi
    24. V. N. Karpushkin, “Bounds for the Betti numbers of a level surface of a harmonic polynomial”, Funct. Anal. Appl., 26:4 (1992), 300–302  mathnet  crossref  mathscinet  zmath  isi
    25. V. N. Karpushkin, “Bounds for Homology Groups of Some Manifolds”, Funct. Anal. Appl., 27:2 (1993), 146–147  mathnet  crossref  mathscinet  zmath  isi
    26. V. N. Karpushkin, “The Number of Components of the Complement of the Level Surface of a Harmonic Polynomial in Three Variables”, Funct. Anal. Appl., 28:2 (1994), 116–118  mathnet  crossref  mathscinet  zmath  isi
    27. Josef Leydold, “On the number of nodal domains of spherical harmonics”, Topology, 35:2 (1996), 301  crossref
    28. V. N. Karpushkin, “The number of components of complements to level surfaces of partially harmonic polynomials”, Math. Notes, 62:6 (1997), 697–700  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    29. Daniel Pecker, “On the geometric genus of projective curves”, Journal of Pure and Applied Algebra, 136:1 (1999), 57  crossref
    30. 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
    31. Ping-xing Sheng, “Hilbert’s sixteenth problem and its generalization”, J of Shanghai Univ, 5:2 (2001), 96  crossref  mathscinet
    32. V. N. Karpushkin, “Number of Components in the Complement to a Level Surface of a Partially Parabolic Polynomial”, Math. Notes, 69:5 (2001), 730–732  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    33. H. S. Y. CHAN, K. W. CHUNG, JIBIN LI, “BIFURCATIONS OF LIMIT CYCLES IN A Z3-EQUIVARIANT VECTOR FIELD OF DEGREE 5”, Int. J. Bifurcation Chaos, 11:08 (2001), 2287  crossref
    34. 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
    35. B. Chevallier, “Four $M$-Curves of Degree $\boldsymbol{8}$”, Funct. Anal. Appl., 36:1 (2002), 76–78  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    36. V. I. Arnol'd, “I. G. Petrovskii, Hilbert's topological problems, and modern mathematics”, Russian Math. Surveys, 57:4 (2002), 833–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    37. V. N. Karpushkin, “On the number of components in the complement of certain algebraic curves”, Russian Math. Surveys, 57:6 (2002), 1228–1229  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    38. JIBIN LI, H. S. Y. CHAN, K. W. CHUNG, “INVESTIGATIONS OF BIFURCATIONS OF LIMIT CYCLES IN Z2-EQUIVARIANT PLANAR VECTOR FIELDS OF DEGREE 5”, Int. J. Bifurcation Chaos, 12:10 (2002), 2137  crossref
    39. 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
    40. J. Math. Sci. (N. Y.), 131:1 (2005), 5366–5380  mathnet  crossref  mathscinet  zmath
    41. Itenberg, I, “Critical points of real polynomials and topology of real algebraic T-surfaces”, Geometriae Dedicata, 101:1 (2003), 61  crossref  mathscinet  zmath  isi
    42. 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
    43. JIBIN LI, “HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS”, Int. J. Bifurcation Chaos, 13:01 (2003), 47  crossref
    44. S. Wang, P. Yu, “Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11”, Chaos, Solitons & Fractals, 30:3 (2006), 606  crossref
    45. SHARON WANG, PEI YU, JIBIN LI, “BIFURCATION OF LIMIT CYCLES IN Z10-EQUIVARIANT VECTOR FIELDS OF DEGREE 9”, Int. J. Bifurcation Chaos, 16:08 (2006), 2309  crossref
    46. Eremenko, A, “On nodal sets and nodal domains on S-2 and R-2”, Annales de l Institut Fourier, 57:7 (2007), 2345  mathscinet  zmath  isi
    47. Hongxian Zhou, Wei Xu, Xiaoshan Zhao, Bingchang Zhou, “Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points”, Applied Mathematics and Computation, 187:2 (2007), 686  crossref
    48. Hongxian Zhou, Wei Xu, Xiaoshan Zhao, Shuang Li, “Detection function method and its application to a class of quintic Hamiltonian systems with quintic perturbations”, Applied Mathematics and Computation, 191:2 (2007), 490  crossref
    49. V. V. Kozlov, “Topology of Real Algebraic Curves”, Funct. Anal. Appl., 42:2 (2008), 98–102  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    50. Teh, JH, “Harnack-Thom theorem for higher cycle groups and picard varieties”, Transactions of the American Mathematical Society, 360:6 (2008), 3263  crossref  mathscinet  zmath  isi
    51. RYAN SCHWARTZ, JÓZSEF SOLYMOSI, FRANK DE ZEEUW, “SIMULTANEOUS ARITHMETIC PROGRESSIONS ON ALGEBRAIC CURVES”, Int. J. Number Theory, 07:04 (2011), 921  crossref
    52. 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
    53. O. O. Vasil'ev, “Study of $D$-decompositions by the methods of computational real-valued algebraic geometry”, Autom. Remote Control, 73:12 (2012), 1978–1993  mathnet  crossref  zmath  isi  elib
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