JournalsjemsVol. 10 , No. 2DOI 10.4171/jems/118

Numerical Campedelli surfaces with fundamental group of order 9

  • Margarida Mendes Lopes

    Instituto Superior Técnico, Lisboa, Portugal
  • Rita Pardini

    Università di Pisa, Italy
Numerical Campedelli surfaces with fundamental group of order 9 cover

Abstract

We give explicit constructions of all the numerical Cam\-pe\-delli surfaces, i.e.\ the minimal surfaces of general type with K2=2K^2=2 and pg=0p_g=0, whose fundamental group has order 9. There are three families, one with \pionealg=Z9\pionealg=\Z_9 and two with \pionealg=Z32\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=Z9\pionealg=\Z_9 and for one of the families of surfaces with \pionealg=Z32\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 K2>1K^2>1 whose bicanonical system has base points.