# Numerical Campedelli surfaces with fundamental group of order 9

Margarida Mendes Lopes; Rita Pardini

Journal of the European Mathematical Society (2008)

- Volume: 010, Issue: 2, page 457-476
- ISSN: 1435-9855

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topMendes 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 -

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