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 : https://doi.org/10.5802/aif.2321
Classification : 14P05,  14P25
Mots clés : réalité totale, fontion méromorphe, courbes réelles sur un ellipsoide, surface K3
@article{AIF_2007__57_6_2015_0,
     author = {Degtyarev, Alex and Ekedahl, Torsten and Itenberg, Ilia and Shapiro, Boris and Shapiro, Michael},
     title = {On total reality of meromorphic functions},
     journal = {Annales de l'Institut Fourier},
     pages = {2015--2030},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {6},
     year = {2007},
     doi = {10.5802/aif.2321},
     mrnumber = {2377894},
     zbl = {1131.14059},
     language = {en},
     url = {archive.numdam.org/item/AIF_2007__57_6_2015_0/}
}
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://archive.numdam.org/item/AIF_2007__57_6_2015_0/

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