Unprojection and deformations of tertiary Burniat surfaces

• Jorge Neves ^[1] ; Roberto Pignatelli ^[2]
  1. [1] Universidade de Coimbra

     Universidade de Coimbra

     Coimbra (Sé Nova), Portugal

     
  2. [2] Universitá di Trento, Italia
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 13, Nº 1, 2014, págs. 225-254
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We construct a 4-dimensional family of surfaces of general type with pg = 0 and K2 = 3 and fundamental group Z/2 ⇥ Q8, where Q8 is the quaternion group. The family constructed contains the Burniat surfaces with K2 = 3.

    Additionally, we construct the universal coverings of the surfaces in our family as complete intersections on (P1)4 and we also give an action of Z/2 ⇥ Q8 on (P1)4 lifting the natural action on the surfaces.

    The strategy is the following. We consider an ´etale (Z/2)3-cover T of a surface with pg = 0 and K2 = 3 and assume that it may be embedded in a Fano 3-fold V. We construct V by using the theory of parallel unprojection. Since V is an Enriques–Fano 3-fold, considering its Fano cover yields the simple description of the above universal covers.