Towards Good Postulation of Fat Points, One Step at a Time
Year: 2025
Type: article
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 $${\mathbb {P}}^n$$ P n 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 $${\mathbb {P}}^n$$ P n and their regularity index. In both cases we report on some complete, or partial, results and conjectures.
Authors: Maria Chiara Brambilla, Elisa Postinghel
Institutions: Marche Polytechnic University, University of Trento
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4408081837