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Resumen de On deformation types of real elliptic surfaces

Alexander Degtyarev Árbol académico, Ilia Itenberg Árbol académico, 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 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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