no. 1
Clifford’s Theorem for real algebraic curves
[Théorème de Clifford pour les courbes algébriques réelles]
Monnier, Jean-Philippe1
1 Université d’Angers Département de Mathématiques 2, boulevard Lavoisier 49045 Angers Cedex 01 (France)
Annales de l'Institut Fourier, Tome 60 (2010) no. 1, pp. 31-50.

On démontre, pour les courbes projectives lisses réelles, une version analogue de l’inégalité de Clifford connue pour les courbes complexes. On étudie aussi très précisément les cas où cette inégalité devient une égalité.

We establish, for smooth projective real curves, an analogue of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.

DOI : 10.5802/aif.2516
Classification : 14C20, 14H51, 14P25, 14P99
Keywords: Real algebraic curves, special divisors
Mot clés : courbes algébriques réelles, diviseurs spéciaux
Monnier, Jean-Philippe 1

1 Université d’Angers Département de Mathématiques 2, boulevard Lavoisier 49045 Angers Cedex 01 (France) 
@article{AIF_2010__60_1_31_0,
     author = {Monnier, Jean-Philippe},
     title = {Clifford{\textquoteright}s {Theorem} for real algebraic curves},
     journal = {Annales de l'Institut Fourier},
     pages = {31--50},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {60},
     number = {1},
     year = {2010},
     doi = {10.5802/aif.2516},
     zbl = {1206.14020},
     mrnumber = {2664309},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2516/}
}
TY  - JOUR
AU  - Monnier, Jean-Philippe
TI  - Clifford’s Theorem for real algebraic curves
JO  - Annales de l'Institut Fourier
PY  - 2010
SP  - 31
EP  - 50
VL  - 60
IS  - 1
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.2516/
DO  - 10.5802/aif.2516
LA  - en
ID  - AIF_2010__60_1_31_0
ER  - 
%0 Journal Article
%A Monnier, Jean-Philippe
%T Clifford’s Theorem for real algebraic curves
%J Annales de l'Institut Fourier
%D 2010
%P 31-50
%V 60
%N 1
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.2516/
%R 10.5802/aif.2516
%G en
%F AIF_2010__60_1_31_0
Monnier, Jean-Philippe. Clifford’s Theorem for real algebraic curves. Annales de l'Institut Fourier, Tome 60 (2010) no. 1, pp. 31-50. doi : 10.5802/aif.2516. http://archive.numdam.org/articles/10.5802/aif.2516/

[1] Accola, R. D. M. On Castelnuovo’s inequality for algebraic curves 1, Trans. Amer. Math. Soc., Volume 251 (1979), pp. 357-373 | MR | Zbl

[2] Accola, Robert D. M. Plane models for Riemann surfaces admitting certain half-canonical linear series. I, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Volume 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 7-20 | MR | Zbl

[3] Arbarello, E.; Cornalba, M.; Griffiths, P. A.; Harris, J. Geometry of Algebraic Curves, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 267, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, 1985 | MR | Zbl

[4] Bochnak, J.; Coste, M.; Roy, M.-F. Géométrie algébrique réelle, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 12, Springer-Verlag, Berlin, 1987 | MR | Zbl

[5] Coppens, M.; Keem, C.; Martens, G. Primitive linear series on curves, Manuscripta Mathematica, Volume 77 (1992), pp. 237-264 | DOI | MR | Zbl

[6] Coppens, M.; Martens, G. Secant space and Clifford’s theorem, Compositio Mathematica, Volume 78 (1991), pp. 193-212 | Numdam | MR | Zbl

[7] Eisenbud, D.; Lange, H.; Martens, G.; Schreyer, F.-O. The Clifford dimension of a projective curve, Compositio Mathematica, Volume 72 (1989), pp. 173-204 | Numdam | MR | Zbl

[8] Gross, B. H.; Harris, J. Real algebraic curves, Ann. Sci. École Norm. Sup. (4), Volume 14 (1981), pp. 157-182 | Numdam | MR | Zbl

[9] Hartshorne, R. Algebraic geometry, Springer-Verlag, New York, 1977 (Graduate Texts in Mathematics, No. 52) | MR | Zbl

[10] Huisman, J. Clifford’s inequality for real algebraic curves, Indag. Math., Volume 14 (2003) no. 2, pp. 197-205 | DOI | MR | Zbl

[11] Monnier, J.-Ph. Divisors on real curves, Adv. Geom., Volume 3 (2003), pp. 339-360 | DOI | MR | Zbl

Cité par Sources :