Numerical Campedelli surfaces with fundamental group of order 9
2008; European Mathematical Society; Volume: 10; Issue: 2 Linguagem: Inglês
10.4171/jems/118
ISSN1435-9863
AutoresMargarida Mendes Lopes, Rita Pardini,
Tópico(s)Polynomial and algebraic computation
ResumoWe 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.
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