Clifford’s Theorem for real algebraic curves

Jean-Philippe Monnier[1]

  • [1] Université d’Angers Département de Mathématiques 2, boulevard Lavoisier 49045 Angers Cedex 01 (France)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 1, page 31-50
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Monnier, Jean-Philippe. "Clifford’s Theorem for real algebraic curves." Annales de l’institut Fourier 60.1 (2010): 31-50. <http://eudml.org/doc/116271>.

@article{Monnier2010,
abstract = {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.},
affiliation = {Université d’Angers Département de Mathématiques 2, boulevard Lavoisier 49045 Angers Cedex 01 (France)},
author = {Monnier, Jean-Philippe},
journal = {Annales de l’institut Fourier},
keywords = {Real algebraic curves; special divisors; real algebraic curves; Clifford inequality},
language = {eng},
number = {1},
pages = {31-50},
publisher = {Association des Annales de l’institut Fourier},
title = {Clifford’s Theorem for real algebraic curves},
url = {http://eudml.org/doc/116271},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Monnier, Jean-Philippe
TI - Clifford’s Theorem for real algebraic curves
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 1
SP - 31
EP - 50
AB - 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.
LA - eng
KW - Real algebraic curves; special divisors; real algebraic curves; Clifford inequality
UR - http://eudml.org/doc/116271
ER -

References

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  1. R. D. M. Accola, On Castelnuovo’s inequality for algebraic curves 1, Trans. Amer. Math. Soc. 251 (1979), 357-373 Zbl0417.14021MR531984
  2. Robert D. M. Accola, 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) 97 (1981), 7-20, Princeton Univ. Press, Princeton, N.J. Zbl0491.30038MR624801
  3. E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris, Geometry of Algebraic Curves, 267 (1985), Springer-Verlag, New York-Berlin-Heidelberg-Tokyo Zbl0559.14017MR770932
  4. J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle, 12 (1987), Springer-Verlag, Berlin Zbl0633.14016MR949442
  5. M. Coppens, C. Keem, G. Martens, Primitive linear series on curves, Manuscripta Mathematica 77 (1992), 237-264 Zbl0786.14016MR1188583
  6. M. Coppens, G. Martens, Secant space and Clifford’s theorem, Compositio Mathematica 78 (1991), 193-212 Zbl0741.14035MR1104787
  7. D. Eisenbud, H. Lange, G. Martens, F.-O. Schreyer, The Clifford dimension of a projective curve, Compositio Mathematica 72 (1989), 173-204 Zbl0703.14020MR1030141
  8. B. H. Gross, J. Harris, Real algebraic curves, Ann. Sci. École Norm. Sup. (4) 14 (1981), 157-182 Zbl0533.14011MR631748
  9. R. Hartshorne, Algebraic geometry, (1977), Springer-Verlag, New York Zbl0367.14001MR463157
  10. J. Huisman, Clifford’s inequality for real algebraic curves, Indag. Math. 14 (2003), 197-205 Zbl1063.14074MR2026814
  11. J.-Ph. Monnier, Divisors on real curves, Adv. Geom. 3 (2003), 339-360 Zbl1079.14013MR1997411

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