On deformation types of real elliptic surfaces

Details On deformation types of real elliptic surfaces On deformation types of real elliptic surfaces

2006-10-02

arxiv.org/abs/math/0610063v2

Amer. J. Math., 130:6 (2008), 1561--1627

Mathematics

Algebraic Geometry

Scientific paper

10.1353/ajm.0.0029

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 $M$- and $(M-1)$- (i.e., maximal and submaximal in the sense of the Smith inequality) curves and surfaces.

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