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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: [email protected]
Roy M. Skjelnes
Affiliation:
Department of Mathematics, KTH, S-100 44 Stockholm, Sweden. E-mail: [email protected]
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Abstract

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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