On Deformation Types of Real Elliptic Surfaces

  title={On Deformation Types of Real Elliptic Surfaces},
  author={A. G. Degtyarev and Ilia Itenberg and Viatcheslav Kharlamov},
We study real elliptic surfaces and trigonal curves (over a base of an arbitrary genus) and their equivariant deformations. We calculate the real TateShafarevich 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. 
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