Generalized Burniat Type surfaces and Bagnera-de Franchis Varieties

Journal of Mathematical Sciences

Bauer, Ingrid¹  Catanese, Fabrizio¹  Frapporti, Davide¹ 

关键词: Surfaces of general type;    topology and connected components of moduli spaces;    abelian varieties;    finite group actions;    Bagnera-de Franchis varieties;    generalized Burniat type surfaces.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Inthisarticleweconstructthreenewfamiliesofsurfacesofgeneraltypewith$p_g=q=0,K^2=6$,andsevennewfamiliesofsurfacesofgeneraltypewith$p_g=q=1,K^2=6$,realizing10newfundamentalgroups.WealsoshowthatthesefamiliescorrespondtopairwisedistinctirreducibleconnectedcomponentsoftheGiesekermodulispaceofsurfacesofgeneraltype.Weachievethisusingtwodifferentmainingredients.Firstweintroduceanewclassofsurfaces,calledgeneralizedBurniattypesurfaces,andwecompletelyclassifythem(andtheconnectedcomponentsofthemodulispacecontainingthem).Second,weintroducethenotionofBagnera-deFranchisvarieties:thesearethefreequotientsofanAbelianvarietybyacyclicgroup(notconsistingonlyoftranslations).Forthesewedevelopsomebasicresults.

【 授权许可】

Unknown