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On Hilbert schemes parameterizing points on the affine line having support in a fixed subset
KTH, Superseded Departments, Mathematics.
2000 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH , 2000. , ii p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-2935OAI: oai:DiVA.org:kth-2935DiVA: diva2:8673
Public defence
2000-03-17, 00:00
Note
QC 20100812Available from: 2000-05-24 Created: 2000-05-24 Last updated: 2010-08-12Bibliographically approved
List of papers
1. The Hilbert scheme parameterizing finite length subschemes of the line with support at the origin
Open this publication in new window or tab >>The Hilbert scheme parameterizing finite length subschemes of the line with support at the origin
2001 (English)In: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 126, no 3, 323-334 p.Article in journal (Refereed) Published
Abstract [en]

We introduce symmetrizing operators of the polynomial ring A[x] in the variable x over a ring A. When A is an algebra over a field k these operators are used to characterize the monic polynomials F(x) of degree n in A[x] such that Ax(k)k[x]((x))/(F(x)) is a free A-module of rank n. We use the characterization to determine the Hilbert scheme parameterizing subschemes of length n of k[x]((x)).

Keyword
Hilbert scheme, finite length subschemes, local rings, symmetrizing, operators, free quotient algebras, points
Identifiers
urn:nbn:se:kth:diva-20562 (URN)000168332700004 ()
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved
2. On the representability of H ilb(n)k x ((x))
Open this publication in new window or tab >>On the representability of H ilb(n)k x ((x))
2000 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 62, 757-770 p.Article in journal (Refereed) Published
Abstract [en]

Let k[x]((x)) be the polynomial ring k[x] localized in the maximal ideal (x) subset of k[x]. The paper studies the Hilbert functor parametrizing ideals of colength n in this ring having support at the origin. The main result is that this functor is not representable. A complete description of the functor as a limit of representable functors is also given.

National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-20405 (URN)000167219900009 ()
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved
3. Symmetric tensors with applications to Hilbert schemes
Open this publication in new window or tab >>Symmetric tensors with applications to Hilbert schemes
1999 (English)Article in journal (Other academic) Submitted
Abstract [en]

Let A[X]_U be a fraction ring of the polynomial ring A[X] in the variable X over a commutative ring A. We show that the Hilbert functor {Hilb}^n_{A[X]_U} is represented by an affine scheme SymmnA(A[X]U) give as the ring of symmetric tensors of ⊗nAA[X]U . The universal family is given as Symmn−1A(A[X]U)×ASpec(A[X]U) .

National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-24061 (URN)
Note

QC 20100812

Available from: 2010-08-12 Created: 2010-08-12 Last updated: 2015-09-23Bibliographically approved

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Citation style
  • apa
  • harvard1
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More styles
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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