The Hilbert scheme parameterizing finite length subschemes of the line with support at the origin

Details The Hilbert scheme parameterizing finite length subschemes of the line with support at the origin The Hilbert scheme parameterizing finite length subschemes of the line with support at the origin

1999-12-17

arxiv.org/abs/math/9912137v1

Mathematics

Algebraic Geometry

Scientific paper

We introduce symmetrizing operators of the polynomial ring $A[x]$ in the varible $x$ 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 $A\otimes_k k[x]_{(x)}/(F(x))$ 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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