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On deformation types of real elliptic surfaces

Alex Degtyarev·Ilia Itenberg·Viatcheslav Kharlamov
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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 $M$- and $(M-1)$- (i.e., maximal and submaximal in the sense of the Smith inequality) curves and surfaces.

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Alex Degtyarev, Ilia Itenberg, Viatcheslav Kharlamov. 2008-07-30. On deformation types of real elliptic surfaces. https://doi.org/10.1353/ajm.0.0029

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