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