Title  Gr\"obner strata in the Hilbert scheme of points. 
Author(s)  Mathias Lederer 
Type  Article in Journal 
Abstract  The present paper shall provide a framework for working with Gr\"obner bases over arbitrary rings k with a prescribed finite standard set Δ. We show that the functor associating to a kalgebra B the set of all reduced Gr\"obner bases with standard set Δ 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 kalgebra B the set of all border bases with standard set Δ and give reasonably small sets of equations defining these schemes. We show that the schemes parametrizing Gr\"obner 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 Gr\"obner bases is not a stratification. 
ISSN  19392346 
File 

URL 
http://arxiv.org/abs/0907.0302 
Language  English 
Journal  J. Commut. Algebra 
Volume  3 
Number  3 
Pages  349404 
Publisher  Rocky Mountain Mathematics Consortium c/o Arizona State University, Tempe, AZ 
Year  2011 
Edition  0 
Translation 
No 
Refereed 
No 