Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/44296
Title: Unprojection and deformations of tertiary Burniat surfaces
Authors: Neves, Jorge 
Pignatelli, Pignatelli 
Issue Date: 2014
Project: info:eu-repo/grantAgreement/FCT/3599-PPCDT/99275/PT 
info:eu-repo/grantAgreement/FCT/5876-PPCDTI/111332/PT 
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.
URI: http://hdl.handle.net/10316/44296
ISSN: 0391173X
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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