Resumen de Involutions on surfaces with P_g=q=1

Carlos Rito

• In this paper some numerical restrictions for surfaces with an involution are obtained. These formulas are used to study surfaces of general typeS withp_g =q = 1 having an involutioni such thatS/i is a nonruled surface and such that the bicanonical map ofS is not composed withi. A complete list of possibilities is given and several new examples are constructed, as bidouble covers of surfaces. In particular the first example of a minimal surface of general type withp_g =q = 1 andK^2 = 7 having birational bicanonical map is obtained.