Numerical Campedelli surfaces with fundamental group of order 9

• Autores: Margarida Mendes Lopes , Rita Pardini
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 10, Nº 2, 2008, págs. 457-476
• Idioma: inglés
• DOI: 10.4171/jems/118
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• Resumen

  • We give explicit constructions of all the numerical Cam\-pe\-delli 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 $\pionealg=\Z_9$ 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 $K^2>1$ whose bicanonical system has base points.