We give explicit constructions of all the numerical Cam\-pe\-delli surfaces, i.e.\ the minimal surfaces of general type with and , whose fundamental group has order 9. There are three families, one with \( \pionealg=\Z_9 \) and two with \( \pionealg=\Z_3^2 \). We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with \( \pionealg=\Z_9 \) and for one of the families of surfaces with \( \pionealg=\Z_3^2 \) the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces of general type with whose bicanonical system has base points.
Cite this article
Margarida Mendes Lopes, Rita Pardini, Numerical Campedelli surfaces with fundamental group of order 9. J. Eur. Math. Soc. 10 (2008), no. 2, pp. 457–476DOI 10.4171/JEMS/118