On total reality of meromorphic functions
[Sur la réalité totale des fonctions méromorphes]
Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 2015-2030.

On montre que, si tous les points critiques d’une fonction méromorphe de degré au plus quatre sur une courbe algébrique réelle de genre arbitraire sont réels, alors la fonction est conjugée à une fonction méromorphe réelle par un automorphisme projectif approprié de l’image.

We show that, if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points, then it is conjugate to a real meromorphic function by a suitable projective automorphism of the image.

DOI : 10.5802/aif.2321
Classification : 14P05, 14P25
Keywords: Total reality, meromorphic function, real curves on ellipsoid, K3-surface
Mot clés : réalité totale, fontion méromorphe, courbes réelles sur un ellipsoide, surface K3
Degtyarev, Alex 1 ; Ekedahl, Torsten 2 ; Itenberg, Ilia 3 ; Shapiro, Boris 2 ; Shapiro, Michael 4

1 Bilkent University Department of Mathematics Bilkent, Ankara 06533 (Turkey)
2 Stockholm University Department of Mathematics SE-106 91 Stockholm (Sweden)
3 Université Louis Pasteur IRMA 7 rue René Descartes 67084 Strasbourg cedex (France)
4 Michigan State University Department of Mathematics East Lansing MI 48824-1027 (USA)
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Degtyarev, Alex; Ekedahl, Torsten; Itenberg, Ilia; Shapiro, Boris; Shapiro, Michael. On total reality of meromorphic functions. Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 2015-2030. doi : 10.5802/aif.2321. http://www.numdam.org/articles/10.5802/aif.2321/

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