Details:
Title  Components of Gr\"obner strata in the Hilbert scheme of points.  Author(s)  Mathias Lederer  Type  Article in Journal  Abstract  We fix the lexicographic order ≺ on the polynomial ring S=k[x1, …, xn] over a ring k. We define Graphic, the moduli space of reduced Gröbner bases with a given finite standard set Δ, and its open subscheme Graphic, 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. We show that analogous statements do not hold for the scheme Graphic. Our results prove a version of a conjecture by Bernd Sturmfels.  ISSN  00246115; 1460244X/e 
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 URL 
http://plms.oxfordjournals.org/content/108/1/187 
Language  English  Journal  Proc. Lond. Math. Soc. (3)  Volume  108  Number  1  Pages  187224  Publisher  Oxford University Press, Oxford; London Mathematical Society, London  Year  2014  Edition  0  Translation 
No  Refereed 
No 
