# Detaching embedded points

@article{Chen2012DetachingEP,
title={Detaching embedded points},
author={Dawei Chen and Scott Nollet},
journal={Algebra \& Number Theory},
year={2012},
volume={6},
pages={731-756}
}
• Published 11 November 2009
• Mathematics
• Algebra & Number Theory
Suppose that XYP N differ at finitely many points: when is Y a flat limit of X union isolated points? Our main result says that this is possible when X is a local complete intersection of codimension 2 and the multiplicities are at most 3. We show by example that no hypothesis can be weakened: the conclusion fails for (a) embedded points of multiplicity > 3, (b) local complete intersections X of codimension > 2 and (c) non-local complete intersections of codimension 2. As applications, we…
10 Citations
Families of Elliptic Curves in P3 and Bridgeland Stability
• Mathematics
Michigan Mathematical Journal
• 2018
We study wall crossings in Bridgeland stability for the Hilbert scheme of elliptic quartic curves in three dimensional projective space. We provide a geometric description of each of the moduli
Moduli of distributions via singular schemes
• Mathematics
Mathematische Zeitschrift
• 2022
Let $X$ be a smooth projective variety with $\operatorname{Pic}(X) \simeq \mathbb{Z}$. We show that the map that sends a codimension one distribution on $X$ to its singular scheme is a morphism from
Geometry of canonical genus four curves
We apply Bridgeland stability conditions machinery to describe the geometry of some classical moduli spaces associated with canonical genus four curves in P via an effective control over its
A G ] 5 O ct 2 02 0 MODULI OF DISTRIBUTIONS VIA SINGULAR SCHEMES
• Mathematics
• 2020
Let X be a smooth projective variety with Pic(X) ≃ Z. We show that the map that sends a codimension one distribution on X to its singular scheme is a morphism from the moduli space of distributions
Hilbert schemes with few Borel fixed points
We characterize Hilbert polynomials that give rise to Hilbert schemes with two Borel fixed points and determine when the associated Hilbert schemes or its irreducible components are non-singular.
Moduli spaces of rank 2 instanton sheaves on the projective space
• Mathematics
• 2017
We study the irreducible components of the moduli space of instanton sheaves on $\mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with $c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In
A local study of the fiber-full scheme
• Mathematics
• 2022
We study some of the local properties of the fiber-full scheme, which is a fine moduli space that generalizes the Hilbert scheme by parametrizing closed subschemes with prescribed cohomological data.
Moduli of Space Sheaves with Hilbert Polynomial 4m + 1
Abstract We investigate the moduli space of sheaves supported on space curves of degree and having Euler characteristic 1. We give an elementary proof of the fact that this moduli space consists of
The Hilbert scheme of a pair of linear spaces
Let $$\mathcal {H}_{a,b}^n$$ H a , b n denote the component of the Hilbert scheme whose general point parameterizes an a -plane union a b -plane meeting transversely in $${\mathbf {P}}^n$$ P n . We

## References

SHOWING 1-10 OF 32 REFERENCES
Hilbert Scheme of a Pair of Codimension Two Linear Subspaces
• Mathematics
• 2009
We study the component H n of the Hilbert scheme whose general point parameterizes a pair of codimension two linear subspaces in ℙ n for n ≥ 3. We show that H n is smooth and isomorphic to the
A filtered Bertini-type theorem.
• Mathematics
• 1989
Let φ: E —» F be a general homomorphism between vector bundles of rank m, n over a smooth variety X, and let Υ be the degeneracy locus of φ. It is well known that if E K ®F is generated by global
On the connectedness of the hilbert scheme of curves in P3
In studying the classification of algebraic curves in the projective 3-space P3 over an algebraically closed field k , one of the earliest problems has been to identify for each choice of degree d
Hilbert Schemes of Degree Four Curves
• Mathematics
Compositio Mathematica
• 2003
In this paper we determine the irreducible components of the Hilbert schemes H4,g of locally Cohen-Macaulay space curves of degree four and arbitrary arithmetic genus g: there are roughly ∼(g2/24) of
Reducibility of the families of 0-dimensional schemes on a variety
AbstractIfA is a regular local ring of dimensionr>2, over an algebraically closed fieldk, we show that the Hilbert scheme HilbnA parametrizing ideals of colengthn inA(dimkA/I=n) has dimension>cn2−2/r
DEFORMATIONS OF SPACE CURVES: CONNECTEDNESS OF HILBERT SCHEMES Dedicated to Paolo Valabrega on the occasion of his 60 th birthday
We survey the Hilbert schemes Hd,g of Cohen-Macaulay space curves having degree d and genus g, giving their geography and the current state of the connectedness problem. Focusing on a specific
Hilbert schemes of 8 points
• Mathematics
• 2009
The Hilbert scheme H^d_n of n points in A^d contains an irreducible component R^d_n which generically represents n distinct points in A^d. We show that when n is at most 8, the Hilbert scheme H^d_n
The genus of space curves
SuntoSi dimostra che seC⊃ℙk3 (k di caratteristica qualunque) é una curva, non piana, localmente Cohen-Macaulay, di gradod, allorapa (C)≤((d−2)(d−3))/2. Si mostra che questa limitazione è ottimale, e
Introduction to Liaison Theory and Deficiency Modules
Part 1 Background: finitely generated graded S-modules the deficiency modules (Mi)(V) hyperplane and hypersurface sections Artinian reductions and h-vectors examples. Part 2 Submodules of the