2012
DOI: 10.2140/ant.2012.6.731
|View full text |Cite
|
Sign up to set email alerts
|

Detaching embedded points

Abstract: We show that if $D \subset \mathbb P^N$ is obtained from a codimension two local complete intersection $C$ by adding embedded points of multiplicity $\leq 3$, then $D$ is a flat limit of $C$ and isolated points. As applications, we determine the irreducible components of Hilbert schemes of space curves with high arithmetic genus, show the smoothness of the Hilbert component whose general member is a plane curve union a point in $\mathbb P^3$, and construct a Hilbert component whose general member has an embedd… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
34
0

Year Published

2017
2017
2023
2023

Publication Types

Select...
7
1

Relationship

0
8

Authors

Journals

citations
Cited by 14 publications
(34 citation statements)
references
References 17 publications
0
34
0
Order By: Relevance
“…To estimate τ (n), we must count the different ways in which an integer n ≥ 3 can be written as n = d 1 d 2 + c with c ≥ 0, and 1 ≤ d 1 ≤ d 2 excluding the pairs (d 1 , d 2 ) = (1, 1), (1,2). Consider the function…”
Section: Moduli Space Of Instanton Sheavesmentioning
confidence: 99%
See 1 more Smart Citation
“…To estimate τ (n), we must count the different ways in which an integer n ≥ 3 can be written as n = d 1 d 2 + c with c ≥ 0, and 1 ≤ d 1 ≤ d 2 excluding the pairs (d 1 , d 2 ) = (1, 1), (1,2). Consider the function…”
Section: Moduli Space Of Instanton Sheavesmentioning
confidence: 99%
“…Next, we consider the following situation: let Σ be an irreducible, nonsingular, complete intersection curve in P 3 , given as the intersection surfaces of degrees d 1 and d 2 , with 1 ≤ d 1 ≤ d 2 and (d 1 , d 2 ) = (1, 1), (1,2), and let Γ be a smooth irreducible rational curve in P 3 of degree m disjoint from Σ.…”
Section: Moduli Space Of Instanton Sheavesmentioning
confidence: 99%
“…As a consequence of Theorem A, we obtain that the Hilbert scheme Hilb 4t (P 3 ) has two components. This is a well known fact (see [CN12,Got08]). More interestingly, the previous result describes what is called the principal component, which parametrizes smooth elliptic curves along with their flat limits.…”
Section: Introductionmentioning
confidence: 75%
“…We achieve this as follows. Using the decomposition of Hilb P 3 (4m + 1) into irreducible components, found in [2], we show that the subset of M of sheaves generated by a global section is irreducible, see Proposition 2.4. This provides our first irreducible component.…”
Section: Introductionmentioning
confidence: 91%
“…where l 1 , l 2 , l 3 are linearly independent. Let R, E ⊂ M 0 be the subsets of sheaves having resolution (1), respectively, (2). Clearly, R is an open subset of M and consists of structure sheaves of rational quartic curves.…”
Section: Introductionmentioning
confidence: 99%