Degtyarev, A.2015-07-282015-07-2820140075-4102http://hdl.handle.net/11693/13133We 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. © De Gruyter 2014.EnglishArticle10.1515/crelle-2012-00201435-5345