Unprojection and deformations of tertiary Burniat surfaces

Details Unprojection and deformations of tertiary Burniat surfaces Unprojection and deformations of tertiary Burniat surfaces

2011-01-17

arxiv.org/abs/1101.3160v3

Mathematics

Algebraic Geometry

29 pages, 3 figures. Final version. To appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Unprojection and deformations of tertiary Burniat surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Unprojection and deformations of tertiary Burniat surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unprojection and deformations of tertiary Burniat surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-285526