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2012 Detaching embedded points
Dawei Chen, Scott Nollet
Algebra Number Theory 6(4): 731-756 (2012). DOI: 10.2140/ant.2012.6.731


Suppose that closed subschemes XYN 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 3.


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Dawei Chen. Scott Nollet. "Detaching embedded points." Algebra Number Theory 6 (4) 731 - 756, 2012.


Received: 17 December 2010; Revised: 10 May 2011; Accepted: 30 June 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1250.14004
MathSciNet: MR2966717
Digital Object Identifier: 10.2140/ant.2012.6.731

Primary: 14B07
Secondary: 14H10 , 14H50

Keywords: embedded points , Hilbert schemes

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.6 • No. 4 • 2012
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