Journal of the European Mathematical Society


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Volume 10, Issue 2, 2008, pp. 457–476
DOI: 10.4171/JEMS/118

Numerical Campedelli surfaces with fundamental group of order 9

Margarida Mendes Lopes[1] and Rita Pardini[2]

(1) Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, LISBOA, PORTUGAL
(2) Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, 56127, PISA, ITALY

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.

Keywords: Campedelli surface, surface with pg=0, fundamental group, torsion

Mendes Lopes M, Pardini R. Numerical Campedelli surfaces with fundamental group of order 9. J. Eur. Math. Soc. 10 (2008), 457-476. doi: 10.4171/JEMS/118