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1 results

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

  • Dan Laksov, Roy M. Skjelnes
  • Journal:
    Compositio Mathematica / Volume 126 / Issue 3 / May 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 323-334
    Print publication:
    May 2001
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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).