Real algebraic curves

Benedict H. Gross; Joe Harris

Annales scientifiques de l'École Normale Supérieure (1981)

  • Volume: 14, Issue: 2, page 157-182
  • ISSN: 0012-9593

How to cite

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Gross, Benedict H., and Harris, Joe. "Real algebraic curves." Annales scientifiques de l'École Normale Supérieure 14.2 (1981): 157-182. <http://eudml.org/doc/82070>.

@article{Gross1981,
author = {Gross, Benedict H., Harris, Joe},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {real theta-characteristics; real abelian varieties; complex conjugation on complex algebraic curves; real curves; Picard scheme; Real hyperelliptic curves; real plane curves; real trigonal curves; real moduli},
language = {eng},
number = {2},
pages = {157-182},
publisher = {Elsevier},
title = {Real algebraic curves},
url = {http://eudml.org/doc/82070},
volume = {14},
year = {1981},
}

TY - JOUR
AU - Gross, Benedict H.
AU - Harris, Joe
TI - Real algebraic curves
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1981
PB - Elsevier
VL - 14
IS - 2
SP - 157
EP - 182
LA - eng
KW - real theta-characteristics; real abelian varieties; complex conjugation on complex algebraic curves; real curves; Picard scheme; Real hyperelliptic curves; real plane curves; real trigonal curves; real moduli
UR - http://eudml.org/doc/82070
ER -

References

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  1. [1] N. A'CAMPO, Sur la première partie du seizième problème de Hilbert (Sém. Bourbaki, exposé 537, 1979). Zbl0451.14019
  2. [2] M. ATIYAH, Riemann Surfaces and Spin Structures (Ann. Éc. Norm. Sup., T. 4, 4e serie, 1971, pp. 47-62). Zbl0212.56402MR44 #3350
  3. [3] P. GRIFFITHS and J. HARRIS, Principles of Algebraic Geometry, New York, Wiley, 1978. Zbl0408.14001MR80b:14001
  4. [4] B. GROSS, Arithmetic on Elliptic Curves with Complex Multiplication (Lecture Notes, No. 776, Springer, 1980). Zbl0433.14032MR81f:10041
  5. [5] A. HURWITZ, Über eindeutige 2n-fach periodische Funktionen (Math. Werke I., 1932, pp. 99-116). 
  6. [6] D. HUSEMOLLER and J. MILNOR, Symmetric Bilinear Forms, New York, Springer, 1973. Zbl0292.10016MR58 #22129
  7. [7] F. KLEIN, On Riemann's Theory of Algebraic Functions and Their Integrals, Cambridge, Macmillan and Bowes, 1893. 
  8. [8] F. KLEIN, Ueber Realitätsverhältnisse bei der einem beliebigen Geschlechte zugehoren Normalcurve der ϕ (Math. Ann., Vol. 42, 1893, pp. 1-29). JFM25.0689.03
  9. [9] S. LANG and J. TATE, Principal Homogeneous Spaces Over Abelian Varieties (Amer. J. Math., Vol. 80, pp. 659-684). Zbl0097.36203MR21 #4960
  10. [10] H. MARTENS, A New Proof of Torelli's Theorem (Annals of Math., Vol. 78 1963, pp. 107-111). Zbl0147.20801MR27 #2506
  11. [11] D. MUMFORD, Theta Characteristics of An Algebraic Curve (Ann. Éc. Norm. Sup., T. 4, 4e série, 1971, pp. 181-192). Zbl0216.05904MR45 #1918
  12. [12] M. SEPPÄLÄ, Quotients of Complex Manifolds and Moduli Spaces of Klein Surfaces (Preprint). Zbl0456.32014
  13. [13] J.-P. SERRE, Groupes algébriques et corps de classes, Hermann, Paris, 1959. Zbl0097.35604MR21 #1973
  14. [14] G. SHIMURA, On the Real Points of an Arithmetic quotient of a Bounded Symmetric Domain (Math. Ann., Vol. 215, 1975, pp. 135-164). Zbl0394.14007MR58 #27992
  15. [15] J. TATE, W.C. Groups Over p-Adic Fields (Sém. Bourbaki, exposé 156, 1957). Zbl0091.33701MR21 #4162
  16. [16] G. WEICHOLD, Uber symmetrische Riemannsche Flachen (Zeit f. Math. u. Phys., Vol. 28, 1883, pp. 321-351). JFM15.0434.01
  17. [17] A. WEIL, The Field of Definition of a Variety (Amer. J. Math., Vol. 78, 1956, pp. 509-524). Zbl0072.16001MR18,601a
  18. [18] G. WILSON, Hilbert's Sixteenth Problem (Topology, Vol. 17, 1978, pp. 53-73). Zbl0394.57001MR58 #16684
  19. [19] E. WITT, Zerlegung reeller algebraischer Funktionen in Quadrate (J. Crelle., Vol. 171, 1934, pp. 4-11). Zbl0009.29103JFM60.0099.01

Citations in EuDML Documents

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  1. Edoardo Ballico, Codimension 1 subvarieties g and real gonality of real curves
  2. Christian Okonek, Andrei Teleman, Symmetric theta divisors of Klein surfaces
  3. Michele Audin, Robert Silhol, Variétés abéliennes réelles et toupie de Kowalevski
  4. Daniel Allcock, James A. Carlson, Domingo Toledo, Hyperbolic geometry and moduli of real cubic surfaces
  5. Jean-Philippe Monnier, Clifford’s Theorem for real algebraic curves
  6. Mika Seppälä, Real algebraic curves in the moduli space of complex curves
  7. J. Bochnak, W. Kucharz, R. Silhol, Morphisms, line bundles and moduli spaces in real algebraic geometry

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