Components of Gröbner strata in the Hilbert scheme of points

@article{Lederer2010ComponentsOG,
  title={Components of Gr{\"o}bner strata in the Hilbert scheme of points},
  author={Mathias Lederer},
  journal={Proceedings of the London Mathematical Society},
  year={2010},
  volume={108}
}
  • M. Lederer
  • Published 18 June 2010
  • Mathematics
  • Proceedings of the London Mathematical Society
We fix the lexicographic order ≺ on the polynomial ring S=k[x1, …, xn] over a ring k. We define HilbS/k≺Δ , the moduli space of reduced Gröbner bases with a given finite standard set Δ, and its open subscheme HilbS/k≺Δ,ét , the moduli space of families of # Δ points whose attached ideal has the standard set Δ. We determine the number of irreducible and connected components of the latter scheme; we show that it is equidimensional over Spec k; and we determine its relative dimension over Spec k… 
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