On the regularity of the monomial point of a border basis scheme
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, cilt.61, sa.3, ss.515-532, 2020 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 61 Sayı: 3
- Basım Tarihi: 2020
- Doi Numarası: 10.1007/s13366-019-00482-7
- Dergi Adı: BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.515-532
- İstanbul Kültür Üniversitesi Adresli: Evet
Özet
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.