English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We call a projective surface \(X\) mixed quasi-étale quotient if there exists a curve \(C\) of genus \(g(C)\ge 2\) and a finite group \(G\) that acts on \(C\times C\) exchanging the factors such that \(X=(C\times C)/G\) and the map \(C\times C \rightarrow X\) 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 \((C\times C)/G^0\) has only nodes as singularities, where \(G^0\triangleleft G\) is the index two subgroup of the elements that do not exchange the factors. We classify the minimal regular surfaces with \(p_g=0\) 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 \(\mathbb{Z }_4\), and we realize 2 new topological types of surfaces of general type. Three of the families we construct are \(\mathbb{Q }\)-homology projective planes.

Mixed quasi-étale surfaces, new surfaces of general type with $$p_g=0$$ and their fundamental group