On the regularity of the monomial point of a border basis scheme
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, vol.61, no.3, pp.515-532, 2020 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 61 Issue: 3
- Publication Date: 2020
- Doi Number: 10.1007/s13366-019-00482-7
- Journal Name: BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Page Numbers: pp.515-532
- Istanbul Kültür University Affiliated: Yes
Abstract
The border basis scheme BO parametrizes all 0-dimensional ideals in K[ x1,..., xn], where K is an arbitrary field, which have a border basis with respect to a given order ideal of terms O. Its vanishing ideal I (BO) is generated by quadratic equations which are easy to describe, and it contains a unique monomial point, namely the point corresponding to the monomial ideal generated by the terms outside O. Based on a detailed study of the generators of I (BO), we describe a K-basis of the cotangent space m/m2, where m is the maximal ideal of the monomial point. Moreover, we provide an efficient algorithm to compute such a basis and use it to characterize the regularity of the monomial point.