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Numerical Campedelli surfaces with fundamental group of order 9

Margarida Mendes Lopes, Rita Pardini (2008)

Journal of the European Mathematical Society

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 π 1 alg = 9 and two with π 1 alg = 3 2 . We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with π 1 alg = 9 and for one of the families of surfaces with π 1 alg = 3 2 the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces of general...

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