Gr\"obner strata in the Hilbert scheme of points

@article{Lederer2009GrobnerSI,
  title={Gr\"obner strata in the Hilbert scheme of points},
  author={Mathias Lederer},
  journal={arXiv: Algebraic Geometry},
  year={2009}
}
  • M. Lederer
  • Published 2 July 2009
  • Mathematics
  • arXiv: Algebraic Geometry
The present paper shall provide a framework for working with Gr\"obner 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 Gr\"obner 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… 

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