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The Hilbert scheme parameterizing finite length subschemes of the line with support at the origin
KTH, Superseded Departments, Mathematics.
KTH, Superseded Departments, Mathematics.
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)).

Place, publisher, year, edition, pages
2001. Vol. 126, no 3, 323-334 p.
Keyword [en]
Hilbert scheme, finite length subschemes, local rings, symmetrizing, operators, free quotient algebras, points
Identifiers
URN: urn:nbn:se:kth:diva-20562ISI: 000168332700004OAI: oai:DiVA.org:kth-20562DiVA: diva2:339258
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved
In thesis
1. On Hilbert schemes parameterizing points on the affine line having support in a fixed subset
Open this publication in new window or tab >>On Hilbert schemes parameterizing points on the affine line having support in a fixed subset
2000 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH, 2000. ii p.
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-2935 (URN)
Public defence
2000-03-17, 00:00
Note
QC 20100812Available from: 2000-05-24 Created: 2000-05-24 Last updated: 2010-08-12Bibliographically approved

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