A simply connected numerical Campedelli surface with an involution

作者：Park Heesang; Shin Dongsoo^*; Urzua Giancarlo

来源：Mathematische Annalen, 2013, 357(1): 31-49.

DOI：10.1007/s00208-013-0905-6

We construct a simply connected minimal complex surface of general type with and 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 and . In order to construct the example, we combine a double covering and -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 Kollar 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 -action.

• 出版日期2013-9