Abstract
We give explicit constructions of all the numerical Campedelli surfaces, i.e. the minimal surfaces of general type with
K^2=2
and
p_g=0
, whose fundamental group has order 9. There are three families, one with
\pi^{\mathrm{alg}}=\mathbb Z_9
and two with
\pi^{\mathrm{alg}}=\mathbb Z_3^2
.
We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with
\pi^{\mathrm{alg}}=\mathbb Z_9
and for one of the families of surfaces with
\pi^{\mathrm{alg}}=\mathbb Z_3^2
the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces of general type with
K^2>1
whose bicanonical system has base points.