no. 6
On total reality of meromorphic functions
Degtyarev, Alex1; Ekedahl, Torsten2; Itenberg, Ilia3; Shapiro, Boris2; Shapiro, Michael4
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)
Annales de l'Institut Fourier, Volume 57 (2007) no. 6, pp. 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: 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, Volume 57 (2007) no. 6, pp. 2015-2030. doi : 10.5802/aif.2321. https://aif.centre-mersenne.org/articles/10.5802/aif.2321/

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