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First steps towards total reality of meromorphic functions.
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Dept. of Maths, Michigan State University.
2006 (English)In: Moscow Mathematical Journal, Vol. 6, no 1Article in journal (Refereed) Published
Abstract [en]

It was earlier conjectured by the second and the third authors that any rational curve γ: CP1 → CPn such that the inverse images of all its flattening points lie on the real line RP1 ⊂ CP1 is real algebraic up to a Möbius transformation of the image CPn. (By a flattening point p on γ we mean a point at which the Frenet n-frame (γ′,γ″,…,γ(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.

Place, publisher, year, edition, pages
2006. Vol. 6, no 1
Keyword [en]
Total reality, meromorphic functions, flattening points
National Category
URN: urn:nbn:se:su:diva-21650OAI: diva2:188177
Available from: 2013-01-30 Created: 2007-12-13 Last updated: 2013-01-30Bibliographically approved

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