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- W1993847568 abstract "The present paper shall provide a framework for working with Grobner bases over arbitrary rings $k$ with a prescribed finite standard set $Delta$. We show that the functor associating to a $k$-algebra $B$ the set of all reduced Grobner bases with standard set $Delta$ is representable and that the representing scheme is a locally closed stratum in the Hilbert scheme of points. We cover the Hilbert scheme of points by open affine subschemes which represent the functor associating to a $k$-algebra $B$ the set of all border bases with standard set $Delta$ and give reasonably small sets of equations defining these schemes. We show that the schemes parametrizing Grobner bases are connected; give a connectedness criterion for the schemes parametrizing border bases; and prove that the decomposition of the Hilbert scheme of points into the locally closed strata parametrizing Grobner bases is not a stratification." @default.
- W1993847568 created "2016-06-24" @default.
- W1993847568 creator A5075949254 @default.
- W1993847568 date "2009-07-02" @default.
- W1993847568 modified "2023-09-27" @default.
- W1993847568 title "Grobner strata in the Hilbert scheme of points" @default.
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