Real trigonal curves and real elliptic surfaces of type I
Algebraic Geometry
2014-06-06 v1
Abstract
We study real trigonal curves and elliptic surfaces of type (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 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 with all singular fibers real.
Keywords
Cite
@article{arxiv.1102.3414,
title = {Real trigonal curves and real elliptic surfaces of type I},
author = {Alex Degtyarev and Ilia Itenberg and Victor Zvonilov},
journal= {arXiv preprint arXiv:1102.3414},
year = {2014}
}