Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 28 Sep 2021 14:29:31 GMT2021-09-28T14:29:31Z5011Unprojection and deformations of tertiary Burniat surfaceshttp://hdl.handle.net/10316/44296Title: Unprojection and deformations of tertiary Burniat surfaces
Authors: Neves, Jorge; Pignatelli, Pignatelli
Abstract: We construct a 4-dimensional family of surfaces of general type with p_g=0
and K^2=3 and fundamental group Z/2xQ_8, where Q_8 is the quaternion group. The
family constructed contains the Burniat surfaces with K^2=3. Additionally, we
construct the universal coverings of the surfaces in our family as complete
intersections on (\PP^1)^4 and we also give an action of Z/2xQ_8 on (\PP^1)^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 p_g=0 and K^2=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 universal covers above.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/442962014-01-01T00:00:00Z