Some bidouble planes with $p_g=q=0$ and $4\leq K^2\leq 7$

TL;DR

This paper classifies certain complex surfaces with specific invariants, constructs examples with particular properties, and describes them as bidouble covers of the plane, expanding understanding of surfaces with $p_g=q=0$ and $4\,\leq\,K^2\leq7$.

Contribution

It provides a list of possible surfaces with $p_g=0$ and constructs explicit examples as bidouble covers, including new cases with $K^2=4$ to $7$.

Findings

Classified surfaces with $p_g=0$ and specific involution properties.

Constructed explicit examples as double coverings of Enriques surfaces.

Described these surfaces as bidouble coverings of the plane.

Abstract

We give a list of possibilities for surfaces of general type with $p_g=0$ having an involution $i$ such that the bicanonical map of $S$ is not composed with $i$ and $S/i$ is not rational. Some examples with $K^2=4,...,7$ are constructed as double coverings of an Enriques surface. These surfaces have a description as bidouble coverings of the plane.