Sur la première partie du seizième problème de Hilbert

Norbert A'Campo

Séminaire Bourbaki (1978-1979)

  • Volume: 21, page 208-227
  • ISSN: 0303-1179

How to cite


A'Campo, Norbert. "Sur la première partie du seizième problème de Hilbert." Séminaire Bourbaki 21 (1978-1979): 208-227. <>.

author = {A'Campo, Norbert},
journal = {Séminaire Bourbaki},
keywords = {16 th Hilbert problem; number of components of real plane curves},
language = {fre},
pages = {208-227},
publisher = {Springer-Verlag},
title = {Sur la première partie du seizième problème de Hilbert},
url = {},
volume = {21},
year = {1978-1979},

AU - A'Campo, Norbert
TI - Sur la première partie du seizième problème de Hilbert
JO - Séminaire Bourbaki
PY - 1978-1979
PB - Springer-Verlag
VL - 21
SP - 208
EP - 227
LA - fre
KW - 16 th Hilbert problem; number of components of real plane curves
UR -
ER -


  1. A. Harnack - Uber die Vieltheiligkeit der ebenen algebraischen Curven, Math. Ann., 10(1876), 189-199. MR1509883JFM08.0317.04
  2. A. Hurwitz - Über Riemannsche Flächen mit gegebenen Verzweigungspunkten, Math. Ann., 39(1891), 1-61. MR1510692JFM23.0429.01
  3. F. Klein - Riemannsche Flächen, Göttingen, 1892. Zbl0605.01021
  4. D. Hilbert - Über die reellen Züge algebraischer Curven, Math. Ann., 38(1891), 115-138. MR1510666JFM23.0753.02
  5. D.A. Gudkov - Construction of a new séries of M-curves, Dokl. Akad. Nank. S.S.S.R., 200(1971), 1269-1272. Zbl0242.14007MR294342
  6. V.I. Arnol'd - The arrangement of the ovals of reaL plane algebraic curves, involutions of four-dimensional manifolds, and the arithmetic of integral quadratic forms, Funkt. Analiz. i ego Pril.5:3(1971), 1-9. Zbl0268.53001MR286790
  7. V.A. Rohlin - Proof of a conjecture of Gudkov, Funkt. Analiz. i ego Pril., 6:2(1972), 62-64. MR296070
  8. R. Thom - Sur l'homologie des variétés algébriques réelles, Differential and combinatorial topology, (A symposium in honor of Marston Morse), Princeton University Press, 1965, 255-265. Zbl0137.42503MR200942
  9. V.M. Kharlamov - The maximum number of components of a surface of degree 4 in RP3 , Funkt. Analiz. i ego Pril., 6(1972), 101 Zbl0276.14019MR313262
  10. D.A. Gudkov and A.D. Krakhnov - Periodicity of the Euler characteristic of real algebraic (M - 1) varieties, Funkt. Analiz. i ego Pril., 7:2(1973), 15-19. Zbl0285.14011MR331402
  11. A. Marin - Quelques remarques sur les courbes algébriques planes réelles, Manuscript, Orsay, 1977. 
  12. N. Kuiper - The quotient space of CP2 by complex conjugation is the four sphere, Math. Ann., 208(1974), 175-177. Zbl0265.52002MR346817
  13. L. Guillou et A. Marin - Une extension d'un théorème de Rohlin sur la signature, C.R. Acad. Sc. Paris, t. 285 (18 juillet 1977). Zbl0361.57018MR440566
  14. Y. Matsumoto - An Elementary Proof of Rohlin's Signature Theorem and its Extension by Guillou and Marin, Séminaire sur les variétés de dimensions3 et 4 , Orsay. 
  15. V.A. Rohlin - A new result in the theory of 4-dimensional manifolds, Soviet. Math. Doklady, 8(1952), 221-224. MR52101
  16. H. Whitney - On the Topology of Differential Manifolds, in Lectures on Topology, Univ. of Michigan Press, 1941, 101-141. Zbl0063.08233MR5300
  17. E.H. Brown - Generalizations of the Kervaire invariant, Ann. of Math., 95(1972), 368-383. Zbl0241.57014MR293642
  18. I. Petrowski - Sur la topologie des courbes réelles et algébriques, C.R. Acad. Sc. Paris, (1933), 1270-1272. Zbl0008.08003
  19. I. Petrowski - On the topology of real plane algebraic curves, Ann. of Math., 239(1938), 189-209. Zbl0018.27004MR1503398
  20. D.A. Gudkov - The topology of real projective algebraic varieties, Uspekhi Math. Nank.29:4(1974), 3-79, (en Russe). Russian Math.Surveys, 29:4(1974), 1-79, (en Anglais). Zbl0316.14018MR399085
  21. G. Wilson - Hilbert's sixteenth problem, Topology, Vol. 17 (1978), 53-73. Zbl0394.57001MR498591

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.