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V. I. Arnold, On the location of ovals of real algebraic plane curves,
  involutions on four-dimensional smooth manifolds, and the arithmetic of
  integral quadratic forms, Funktsional. Anal. i Prilozhen 5 (1971),
  1-9 (Russian), English  translation in Functional Anal. Appl.
5 (1971), 169-176.
- 2
- 
D. A. Gudkov and G. A. Utkin, The topology of curves of degree  and
  surfaces of degree and
  surfaces of degree , Uchen. Zap. Gorkov. Univ., vol. 87, 1969 (Russian),
  English transl., Transl. AMS 112. , Uchen. Zap. Gorkov. Univ., vol. 87, 1969 (Russian),
  English transl., Transl. AMS 112.
- 3
- 
D. A. Gudkov and A. D. Krakhnov, On the periodicity of the Euler
  characteristic of real algebraic  -manifolds, Funktsional.
Anal.  i Prilozhen. 7 (1973), 15-19 (Russian), English  translation in
  Functional Anal. Appl. 7 (1971). -manifolds, Funktsional.
Anal.  i Prilozhen. 7 (1973), 15-19 (Russian), English  translation in
  Functional Anal. Appl. 7 (1971).
- 4
- 
B. Haas, Les multilucarnes: Nouveaux countre-exemples à la
conjecture de Ragsdale, (to appear in C. R. Acad. Sci. Paris).
- 5
- 
A. Harnack, Über Vieltheiligkeit der ebenen algebraischen Curven, Math.
  Ann. 10 (1876), 189-199.
- 6
- 
D. Hilbert, Über die reellen Züge algebraischen Curven, Math. Ann.
  38 (1891), 115-138.
- 7
- 
D. Hilbert, Mathematische Probleme, Arch. Math. Phys. 3 (1901),
  213-237 (German).
- 8
- 
I. Itenberg, Countre-ememples à la conjecture de Ragsdale, C.
  R. Acad. Sci. Paris 317, Serie I (1993), 277-282.
- 9
- 
V. M. Kharlamov, New congruences for the Euler characteristic of real
  algebraic varieties, Funktsional. Anal. i Prilozhen. 7 (1973), 74-78
  (Russian), English  translation in  Functional Anal. Appl.   7 (1973).
- 10
- 
I. Newton, Enumeratio linearum tertii ordinis, London (1704).
- 11
- 
I. Petrovsky, Sur le topologie des courbes réelles et
algèbriques, C.  R. Acad. Sci. Paris (1933), 1270-1272.
- 12
- 
I. Petrovsky, On the topology of real plane algebraic curves, Ann. of
  Math. 39 (1938), 187-209.
- 13
- 
J.-J. Risler, Construction d'hypersurfaces réelles (d'après
Viro), Séminaire N. Bourbaki (1992), no. 763.
- 14
- 
V. Ragsdale, On the arrangement of the real branches of plane algebraic
  curves, Amer. J. Math. 28 (1906), 377-404.
- 15
- 
V. A. Rokhlin, Congruences modulo  in Hilbert's sixteenth problem,
  Funktsional. Anal. i Prilozhen. 6 (1972), 58-64 (Russian),
 English  translation in Functional Anal. Appl. 6 (1972),
301-306. in Hilbert's sixteenth problem,
  Funktsional. Anal. i Prilozhen. 6 (1972), 58-64 (Russian),
 English  translation in Functional Anal. Appl. 6 (1972),
301-306.
- 16
- 
O. Ya. Viro, Curves of degree 7, curves of degree 8 and the Ragsdale
  conjecture, Dokl. Akad. Nauk SSSR 254 (1980), 1305-1310
  (Russian),  English  translation in Soviet Math. Dokl. 22
  (1980), 566-570.
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- 
O. Viro, Gluing of plane real algebraic curves and constructions
of curves of degrees  and and Lecture Notes in Math. 1060
(1984), Springer-Verlag,  187-200. Lecture Notes in Math. 1060
(1984), Springer-Verlag,  187-200.
- 18
- 
O. Ya. Viro, Plane real algebraic curves: constructions with controlled
  topology, Algebra i analiz 1 (1989), 1-73 (Russian), English
  translation in Leningrad Math. J. 1:5, 1990, 1059-1134.
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