We give an overview on the landscape of polynomial interpolation theory. We will describe first the geometric approach, based on the base locus analysis of linear systems of hypersurfaces of with given degree and assigned multiplicity at a set of points. Secondly, we will consider the algebraic counterpart, with a discussion on the good postulation of fat point schemes of and their regularity index. In both cases we report on some complete, or partial, results and conjectures.
Towards Good Postulation of Fat Points, One Step at a Time / Brambilla, Maria Chiara; Postinghel, Elisa. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - STAMPA. - (2025). [Epub ahead of print] [10.1007/s40574-025-00468-5]
Towards Good Postulation of Fat Points, One Step at a Time
Maria Chiara Brambilla;
2025-01-01
Abstract
We give an overview on the landscape of polynomial interpolation theory. We will describe first the geometric approach, based on the base locus analysis of linear systems of hypersurfaces of with given degree and assigned multiplicity at a set of points. Secondly, we will consider the algebraic counterpart, with a discussion on the good postulation of fat point schemes of and their regularity index. In both cases we report on some complete, or partial, results and conjectures.| File | Dimensione | Formato | |
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