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arXiv · 1102.3414

Real trigonal curves and real elliptic surfaces of type I

Alex Degtyarev·Ilia Itenberg·Victor Zvonilov
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Abstract

We study real trigonal curves and elliptic surfaces of type $\I$ (over a base of an arbitrary genus) and their fiberwise equivariant deformations. The principal tool is a real version of Grothendieck's \emph{dessins d'enfants}. We give a description of maximally inflected trigonal curves of type $\I$ in terms of the combinatorics of sufficiently simple graphs and, in the case of the rational base, obtain a complete classification of such curves. As a consequence, these results lead to conclusions concerning real Jacobian elliptic surfaces of type $\I$ with all singular fibers real.

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Alex Degtyarev, Ilia Itenberg, Victor Zvonilov. 2011-02-16. Real trigonal curves and real elliptic surfaces of type I. https://arxiv.org/abs/1102.3414

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