# 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} }

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

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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

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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

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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

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- 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

- Mathematics
- 2019

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

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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

- MathematicsCanadian Mathematical Bulletin
- 2018

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

- MathematicsMathematische Zeitschrift
- 2021

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…

Schematic union of (n − 3) and (n − 2) dimensional quadrics in Pn

- MathematicsBulletin des Sciences Mathématiques
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