Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-22T19:30:28.565Z Has data issue: false hasContentIssue false
  • English
  • Français

The Hilbert Scheme Parameterizing Finite Length Subschemes of the Line with Support at the Origin

Published online by Cambridge University Press:  04 December 2007

Dan Laksov  and
Roy M. Skjelnes
Dan Laksov
Affiliation:
Department of Mathematics, KTH, S-100 44 Stockholm, Sweden. E-mail: laksov@math.kth.se
Roy M. Skjelnes
Affiliation:
Department of Mathematics, KTH, S-100 44 Stockholm, Sweden. E-mail: skjelnes@math.kth.se
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 A[otimes ]kk[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).

Keywords

Hilbert schemefinite length subschemeslocal ringssymmetrizing operatorsfree quotient algebras
Type
Research Article
Information
Compositio Mathematica , Volume 126 , Issue 3 , May 2001 , pp. 323 - 334
Copyright
© 2001 Kluwer Academic Publishers