On deformation types of real elliptic surfaces
Algebraic Geometry
2009-02-13 v2
Abstract
We study real elliptic surfaces and trigonal curves (over a base of an arbitrary genus) and their equivariant deformations. We calculate the real Tate-Shafarevich group and reduce the deformation classification to the combinatorics of a real version of Grothendieck's {\it dessins d'enfants}. As a consequence, we obtain an explicit description of the deformation classes of - and - (i.e., maximal and submaximal in the sense of the Smith inequality) curves and surfaces.
Cite
@article{arxiv.math/0610063,
title = {On deformation types of real elliptic surfaces},
author = {Alex Degtyarev and Ilia Itenberg and Viatcheslav Kharlamov},
journal= {arXiv preprint arXiv:math/0610063},
year = {2009}
}