| 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 k-algebra 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 k-algebra 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 | 1939-2346 |
| File |
|
| URL |
http://arxiv.org/abs/0907.0302 |
| Language | English |
| Journal | J. Commut. Algebra |
| Volume | 3 |
| Number | 3 |
| Pages | 349--404 |
| Publisher | Rocky Mountain Mathematics Consortium c/o Arizona State University, Tempe, AZ |
| Year | 2011 |
| Edition | 0 |
| Translation |
No |
| Refereed |
No |
