First steps towards total reality of meromorphic functions

T. Ekedahl; B. Shapiro; M. Shapiro

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First steps towards total reality of meromorphic functions

T. Ekedahl·B. Shapiro·M. Shapiro

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Abstract

It was earlier conjectured by the second and the third authors that any rational curve $g:{\mathbb C}P^1\to {\mathbb C}P^n$ such that the inverse images of all its flattening points lie on the real line ${\mathbb R}P^1\subset {\mathbb C}P^1$ is real algebraic up to a linear fractional transformation of the image ${\mathbb C}P^n$. (By a flattening point $p$ on $g$ we mean a point at which the Frenet $n$-frame $(g',g'',...,g^{(n)})$ 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.

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BibTeX RIS

T. Ekedahl, B. Shapiro, M. Shapiro. 2006-05-02. First steps towards total reality of meromorphic functions. https://arxiv.org/abs/math/0605075

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