2011/05/06 by Davide Frapporti, Frapporti, Davide
Mathematics · #14J29 #14Q10 #14Q99 #20F05 #20F34 #58E40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14J29 #msc:14Q10 #msc:14Q99 #msc:20F05 #msc:20F34 #msc:58E40
paper · pdf · doi:10.48550/arxiv.1105.1259
18 pages, 3 tables, v2: change title, exposition improved; v3: minor corrections, final version to be published in Collectanea Mathematica
openalex publication_date 2011/05/06 · arxiv created 2013/04/23 · arxiv updated 2013/04/24 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We call a projective surface X mixed quasi-étale quotient if there exists a curve C of genus g(C)≥ 2 and a finite group G that acts on C× C exchanging the factors such that X=(C× C)/G and the map C× C → X has finite branch locus. The minimal resolution of its singularities is called mixed quasi-étale surface. We study the mixed quasi-étale surfaces under the assumption that (C× C)/G0 has only nodes as singularities, where G0\triangleleft G is the index two subgroup of the elements that do not exchange the factors. We classify the minimal regular surfaces with pg=0 whose canonical model is a mixed quasi-étale quotient as above. All these surfaces are of general type and as an important byproduct, we provide an example of a numerical Campedelli surface with topological fundamental group \bbZ4, and we realize 2 new topological types of surfaces of general type. Three of the families we construct are \bbQ-homology projective planes.