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On deformation types of real elliptic surfaces
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 130, Number 6, December 2008
- pp. 1561-1627
- 10.1353/ajm.0.0029
- Article
- Additional Information
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.