Numerical Campedelli surfaces with fundamental group of order 9

Mendes Lopes, Margarida, and Pardini, Rita. "Numerical Campedelli surfaces with fundamental group of order 9." Journal of the European Mathematical Society 010.2 (2008): 457-476. <http://eudml.org/doc/277435>.

@article{MendesLopes2008,
abstract = {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 $\pi ^\{\text\{alg\}\}_1=\mathbb \{Z\}_9$ and two with $\pi ^\{\text\{alg\}\}_1=\mathbb \{Z\}_3^2$. We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with $\pi ^\{\text\{alg\}\}_1=\mathbb \{Z\}_9$ and for one of the families of surfaces with $\pi ^\{\text\{alg\}\}_1=\mathbb \{Z\}_3^2$ 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.},
author = {Mendes Lopes, Margarida, Pardini, Rita},
journal = {Journal of the European Mathematical Society},
keywords = {Campedelli surface; surface with $p_g=0$; fundamental group; torsion; Numerical Campedelli surfaces; algebraic fundamental group; moduli spaces},
language = {eng},
number = {2},
pages = {457-476},
publisher = {European Mathematical Society Publishing House},
title = {Numerical Campedelli surfaces with fundamental group of order 9},
url = {http://eudml.org/doc/277435},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Mendes Lopes, Margarida
AU - Pardini, Rita
TI - Numerical Campedelli surfaces with fundamental group of order 9
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 2
SP - 457
EP - 476
AB - 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 $\pi ^{\text{alg}}_1=\mathbb {Z}_9$ and two with $\pi ^{\text{alg}}_1=\mathbb {Z}_3^2$. We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with $\pi ^{\text{alg}}_1=\mathbb {Z}_9$ and for one of the families of surfaces with $\pi ^{\text{alg}}_1=\mathbb {Z}_3^2$ 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.
LA - eng
KW - Campedelli surface; surface with $p_g=0$; fundamental group; torsion; Numerical Campedelli surfaces; algebraic fundamental group; moduli spaces
UR - http://eudml.org/doc/277435
ER -