JournalsjemsVol. 10, No. 2pp. 457–476

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
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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.

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. 457–476

DOI 10.4171/JEMS/118