2011/08/03 by Park, Heesang, Shin, Dongsoo, Urzua, Giancarlo
#14J10 #14J17 #14J29 #53D05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1108.0797
We construct a simply connected minimal complex surface of general type with pg=0 and K2=2 which has an involution such that the minimal resolution of the quotient by the involution is a simply connected minimal complex surface of general type with pg=0 and K2=1. In order to construct the example, we combine a double covering and ℚ-Gorenstein deformation. Especially, we develop a method for proving unobstructedness for deformations of a singular surface by generalizing a result of Burns and Wahl which characterizes the space of first order deformations of a singular surface with only rational double points. We describe the stable model in the sense of Kollár and Shepherd-Barron of the singular surfaces used for constructing the example. We count the dimension of the invariant part of the deformation space of the example under the induced ℤ/2ℤ-action.