On deformation types of real elliptic surfaces
American Journal of Mathematics
The Johns Hopkins University Press
1561 - 1627
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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 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. © 2008 by The Johns Hopkins University Press.