# Curves on a double surface.

Scott Nollet; Enrico Schlesinger

Collectanea Mathematica (2003)

- Volume: 54, Issue: 3, page 327-340
- ISSN: 0010-0757

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topNollet, 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 -

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