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

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Compositio Mathematica

Abstract

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⊗ 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).

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References

  1. Briançon, J.: Description de HilbnC(x, y), Invent. Math. 41(1) (1977), 45–89.

    Google Scholar 

  2. Briançon, J. and Iarrobino, A. A.: Dimension of the punctual Hilbert scheme, J. Algebra 55(2) (1978), 536–544.

    Google Scholar 

  3. Coppens, M.: The fat locus of Hilbert schemes of points, Proc. Amer. Math. Soc. 118(3) (1993), 777–783.

    Google Scholar 

  4. Granger, M.: Géométrie des schémas de Hilbert ponctuels, Mém. Soc. Math. France. (N.S.) 8 (1983), 84.

    Google Scholar 

  5. Iarrobino, A. A.: Punctual Hilbert schemes, Mem. Amer. Math. Soc. 10 (1977).

  6. Iarrobino, A. A.: Punctual Hilbert schemes, Bull. Amer.Math. Soc. 78 (1972), 819–823.

    Google Scholar 

  7. Iarrobino, A. A.: Hilbert scheme of points: overview of last ten years, In: Algebraic Geometry (Bowdoin 1985), Proc. Sympos. Pure Math. 46, part 2, Amer. Math. Soc. Providence, RI, 1987, pp. 297–320.

  8. Paxia, G.: On £at families of fat points, Proc. Amer. Math. Soc. 112(1) (1991), 19–23.

    Google Scholar 

  9. Skjelnes, R. M.: On the representability of Hilbnk.[x]..x., J. London Math. Soc. (2) 62(3) (2000), 757–770.

    Google Scholar 

  10. Skjelnes, R. M.: Symmetric tensors with applications to Hilbert schemes, To appear (1999).

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Authors and Affiliations

  1. Department of Mathematics, KTH, S-100 44, Stockholm, Sweden

    Dan Laksov

  2. Department of Mathematics, KTH, S-100 44, Stockholm, Sweden

    Roy M. Skjelnes

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  1. Dan Laksov
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  2. Roy M. Skjelnes
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Laksov, D., Skjelnes, R.M. The Hilbert Scheme Parameterizing Finite Length Subschemes of the Line with Support at the Origin. Compositio Mathematica 126, 323–334 (2001). https://doi.org/10.1023/A:1017552014275

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  • DOI: https://doi.org/10.1023/A:1017552014275

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