Let F be a smooth projective surface contained in a smooth threefold T, and let X be the scheme corresponding to the divisor 2F on T. A locally Cohen-Macaulay curve C included in X gives rise to two effective divisors on F, namely the largest divisor P contained in C intersection F and the curve R residual to C intersection F in C. We show that under suitable hypotheses a general deformation of R and P lifts to a deformation of C on X, and give applications to the study of Hilbert schemes of locally Cohen-Macaulay space curves.
@article{urn:eudml:doc:44322,
title = {Curves on a double surface.},
journal = {Collectanea Mathematica},
volume = {54},
year = {2003},
pages = {327-340},
mrnumber = {MR2010793},
zbl = {1049.14001},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44322}
}
Nollet, Scott; Schlesinger, Enrico. Curves on a double surface.. Collectanea Mathematica, Tome 54 (2003) pp. 327-340. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44322/