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TitleThe geometry of border bases
Author(s) Martin Kreuzer, Lorenzo Robbiano
TypeArticle in Journal
AbstractIn this paper we continue the study of the border basis scheme we started in Kreuzer and Robbiano (2008) [16]. The main topic is the construction of various explicit flat families of border bases. To begin with, we cover the punctual Hilbert scheme Hilb μ ( A n ) by border basis schemes and work out the base changes. This enables us to control flat families obtained by linear changes of coordinates. Next we provide an explicit construction of the principal component of the border basis scheme, and we use it to find flat families of maximal dimension at each radical point. Finally, we connect radical points to each other and to the monomial point via explicit flat families on the principal component.
URL http://www.sciencedirect.com/science/article/pii/S0022404910002628
JournalJournal of Pure and Applied Algebra
Pages2005 - 2018
Translation No
Refereed No