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 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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Schedule a callMore From: Journal für die reine und angewandte Mathematik (Crelles Journal)
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