Unexpected hypersurfaces with multiple fat points. (March 2022)

• Record Type: Journal Article
• Authors: Szpond, Justyna
• Is Part Of: Journal of symbolic computation. Volume 109(2022)
• Page Start: 510
• Page End: 519
• Publication Date: 2022-03
• Subjects: 14C20 -- 14J26 -- 14N20 -- 13A15 -- 13F20; Fat points -- Linear systems -- Postulation problem -- Unexpected hypersurfaces -- Fermat-type arrangements; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.07.018
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Starting with the ground-breaking work of Cook II, Harbourne, Migliore and Nagel, there has been a lot of interest in unexpected hypersurfaces. In the last couple of months a considerable number of new examples and new phenomena has been observed and reported on. All examples studied so far had just one fat point. In this note we introduce a new series of examples, which establishes for the first time the existence of unexpected hypersurfaces with multiple fat points. The key underlying idea is to study Fermat-type configurations of points in projective spaces.