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TitleComponents of Gr\"obner strata in the Hilbert scheme of points.
Author(s) Mathias Lederer
TypeArticle in Journal
AbstractWe 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.
ISSN0024-6115; 1460-244X/e
File
URL http://plms.oxfordjournals.org/content/108/1/187
LanguageEnglish
JournalProc. Lond. Math. Soc. (3)
Volume108
Number1
Pages187--224
PublisherOxford University Press, Oxford; London Mathematical Society, London
Year2014
Edition0
Translation No
Refereed No
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