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Mosc. Math. J., 2006, Volume 6, Number 1, Pages 95–106 (Mi mmj237)  

This article is cited in 3 scientific papers (total in 3 papers)

First steps towards total reality of meromorphic functions

T. Ekedahla, B. Z. Shapiroa, M. Z. Shapirob

a Stockholm University
b Michigan State University

Abstract: It was earlier conjectured by the second and the third authors that any rational curve $\gamma\colon\mathbb{CP}^1\to\mathbb{CP}^n$ such that the inverse images of all its flattening points lie on the real line $\mathbb{RP}^1\subset\mathbb{CP}^1$ is real algebraic up to a Möbius transformation of the image $\mathbb C\mathbb P^n$. (By a flattening point $p$ on $\gamma$ we mean a point at which the Frenet $n$-frame $(\gamma',\gamma",…,\gamma^{(n)})$ is degenerate.) Below we extend this conjecture to the case of meromorphic functions on real algebraic curves of higher genera and settle it for meromorphic functions of degrees 2, 3 and several other cases.

Key words and phrases: Total reality, meromorphic functions, flattening points.

DOI: https://doi.org/10.17323/1609-4514-2006-6-1-95-106

Full text: http://www.ams.org/.../abst6-1-2006.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 14P05, 14P25
Received: December 1, 2005
Language:

Citation: T. Ekedahl, B. Z. Shapiro, M. Z. Shapiro, “First steps towards total reality of meromorphic functions”, Mosc. Math. J., 6:1 (2006), 95–106

Citation in format AMSBIB
\Bibitem{EkeShaSha06}
\by T.~Ekedahl, B.~Z.~Shapiro, M.~Z.~Shapiro
\paper First steps towards total reality of meromorphic functions
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 1
\pages 95--106
\mathnet{http://mi.mathnet.ru/mmj237}
\crossref{https://doi.org/10.17323/1609-4514-2006-6-1-95-106}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2265949}
\zmath{https://zbmath.org/?q=an:1126.14064}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595700006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Degtyarev A., Ekedahl T., Itenberg I., Shapiro B., Shapiro M., “On total reality of meromorphic functions”, Ann Inst Fourier (Grenoble), 57:6 (2007), 2015–2030  crossref  mathscinet  zmath  isi
    2. Mukhin E., Tarasov V., Varchenko A., “The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz”, Ann. of Math. (2), 170:2 (2009), 863–881  crossref  mathscinet  zmath  isi  scopus
    3. Degtyarev A., “Toward a Generalized Shapiro and Shapiro Conjecture”, Perspectives in Analysis, Geometry, and Topology: on the Occasion of the 60th Birthday of Oleg Viro, Progress in Mathematics, 296, eds. Itenberg I., Joricke B., Passare M., Birkhauser Verlag Ag, 2012, 67–79  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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