Detaching embedded points

Chen, Dawei; Nollet, Scott

doi:10.2140/ant.2012.6.731

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Detaching embedded points

Dawei Chen and Scott Nollet

Vol. 6 (2012), No. 4, 731–756

DOI: 10.2140/ant.2012.6.731

Abstract

Suppose that closed subschemes $X \subset Y \subset ℙ^{N}$ differ at finitely many points: when is $Y$ a flat specialization of $X$ union isolated points? Our main result says that this holds if $X$ is a local complete intersection of codimension two and the multiplicity of each embedded point of $Y$ is at most three. We show by example that no hypothesis can be weakened: the conclusion fails for embedded points of multiplicity greater than three, for local complete intersections $X$ of codimension greater than two, and for nonlocal complete intersections of codimension two. As applications, we determine the irreducible components of Hilbert schemes of space curves with high arithmetic genus and show the smoothness of the Hilbert component whose general member is a plane curve union a point in $ℙ^{3}$ .

Keywords

Hilbert schemes, embedded points

Mathematical Subject Classification 2010

Primary: 14B07

Secondary: 14H10, 14H50

Milestones

Received: 17 December 2010

Revised: 10 May 2011

Accepted: 30 June 2011

Published: 25 July 2012

Authors

Dawei Chen
Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago 851 S. Morgan St. Chicago, IL 60607 United States	Department of Mathematics Boston College Chestnut Hill, MA 02467 United States

Scott Nollet
Department of Mathematics Texas Christian University Box 298900 Fort Worth, TX 76129 United States

Vol. 6, No. 4, 2012