In this article we suggest a new approach to the systematic, computer-aided construction and to the classification of product-quotient surfaces, introducing a new invariant, the integer γ, which depends only on the singularities of the quotient model X=(C1×C2)/G. It turns out that γ is related to the codimension of the subspace of H1,1 generated by algebraic curves coming from the construction (i.e., the classes of the two fibers and the Hirzebruch-Jung strings arising from the minimal resolution of singularities of X).
1
Universität Bayreuth, Germany
2
Università di Trento, Italy
Ingrid Bauer; Roberto Pignatelli. Product-quotient surfaces: new invariants and algorithms. Groups, geometry, and dynamics, Tome 10 (2016) no. 1, pp. 319-363. doi: 10.4171/ggd/351
@article{10_4171_ggd_351,
author = {Ingrid Bauer and Roberto Pignatelli},
title = {Product-quotient surfaces: new invariants and algorithms},
journal = {Groups, geometry, and dynamics},
pages = {319--363},
year = {2016},
volume = {10},
number = {1},
doi = {10.4171/ggd/351},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/351/}
}
TY - JOUR
AU - Ingrid Bauer
AU - Roberto Pignatelli
TI - Product-quotient surfaces: new invariants and algorithms
JO - Groups, geometry, and dynamics
PY - 2016
SP - 319
EP - 363
VL - 10
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/351/
DO - 10.4171/ggd/351
ID - 10_4171_ggd_351
ER -
%0 Journal Article
%A Ingrid Bauer
%A Roberto Pignatelli
%T Product-quotient surfaces: new invariants and algorithms
%J Groups, geometry, and dynamics
%D 2016
%P 319-363
%V 10
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/351/
%R 10.4171/ggd/351
%F 10_4171_ggd_351
