On total reality of meromorphic functions
Annales de l'Institut Fourier, Volume 57 (2007) no. 6, p. 2015-2030

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.

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.

DOI : https://doi.org/10.5802/aif.2321
Classification:  14P05,  14P25
Keywords: Total reality, meromorphic function, real curves on ellipsoid, K3-surface
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {6},
     year = {2007},
     pages = {2015-2030},
     doi = {10.5802/aif.2321},
     mrnumber = {2377894},
     zbl = {1131.14059},
     language = {en},
     url = {http://www.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, Volume 57 (2007) no. 6, pp. 2015-2030. doi : 10.5802/aif.2321. http://www.numdam.org/item/AIF_2007__57_6_2015_0/

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