Macaulay-like marked bases
| Autor: | Bertone, Cristina, Cioffi, Francesca, Roggero, Margherita |
|---|---|
| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Journal of Algebra and its Applications, Volume 16, Issue 5, 1 May 2017, Article number 1750100 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S0219498817501006 |
| Popis: | We define marked sets and bases over a quasi-stable ideal $\mathfrak j$ in a polynomial ring on a Noetherian $K$-algebra, with $K$ a field of any characteristic. The involved polynomials may be non-homogeneous, but their degree is bounded from above by the maximum among the degrees of the terms in the Pommaret basis of $\mathfrak j$ and a given integer $m$. Due to the combinatorial properties of quasi-stable ideals, these bases behave well with respect to homogenization, similarly to Macaulay bases. We prove that the family of marked bases over a given quasi-stable ideal has an affine scheme structure, is flat and, for large enough $m$, is an open subset of a Hilbert scheme. Our main results lead to algorithms that explicitly construct such a family. We compare our method with similar ones and give some complexity results. Comment: 30 pages. Final version. In the present version Section 6 about flatness is improved, and new subsections concerning comparison with other existing computational methods (Section 7.1) and some complexity results (Section 7.2) were added |
| Databáze: | arXiv |
| Externí odkaz: |
|