Curves on a double surface.

Nollet, Scott, and Schlesinger, Enrico. "Curves on a double surface.." Collectanea Mathematica 54.3 (2003): 327-340. <http://eudml.org/doc/44322>.

@article{Nollet2003,
abstract = {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.},
author = {Nollet, Scott, Schlesinger, Enrico},
journal = {Collectanea Mathematica},
keywords = {Curvas; Superficies; Deformación; Hilbert schemes; nonreduced surfaces; projective curves},
language = {eng},
number = {3},
pages = {327-340},
title = {Curves on a double surface.},
url = {http://eudml.org/doc/44322},
volume = {54},
year = {2003},
}

TY - JOUR
AU - Nollet, Scott
AU - Schlesinger, Enrico
TI - Curves on a double surface.
JO - Collectanea Mathematica
PY - 2003
VL - 54
IS - 3
SP - 327
EP - 340
AB - 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.
LA - eng
KW - Curvas; Superficies; Deformación; Hilbert schemes; nonreduced surfaces; projective curves
UR - http://eudml.org/doc/44322
ER -