On deformation types of real elliptic surfaces

• Autores: Alexander Degtyarev , Ilia Itenberg , Viatcheslav Kharlamov
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 130, Nº 6, 2008, págs. 1561-1627
• Idioma: inglés
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• Resumen

  • 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.