Locally analytically, any isolated double point occurs as a double cover of a smooth surface. It can be desingularized explicitly via the canonical resolution, as it is very well-known. In this paper we explicitly compute the fundamental cycle of both the canonical and minimal resolution of a double point singularity and we classify those for which the fundamental cycle differs from the fiber cycle. Moreover we compute the conditions that a double point singularity imposes to pluricanonical systems.
@article{urn:eudml:doc:42869,
title = {Explicit resolutions of double point singularities of surfaces.},
journal = {Collectanea Mathematica},
volume = {53},
year = {2002},
pages = {99-131},
zbl = {1043.14007},
mrnumber = {MR1913513},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42869}
}
Calabri, Alberto; Ferraro, Rita. Explicit resolutions of double point singularities of surfaces.. Collectanea Mathematica, Tome 53 (2002) pp. 99-131. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42869/