Strict inclusions of high rank loci. (March 2022)

• Record Type: Journal Article
• Authors: Ballico, Edoardo; Bernardi, Alessandra; Ventura, Emanuele
• Is Part Of: Journal of symbolic computation. Volume 109(2022)
• Page Start: 238
• Page End: 249
• Publication Date: 2022-03
• Subjects: primary 14N07 14N05 15A72; High tensor rank -- Symmetric tensor rank -- Zero-dimensional schemes -- Cactus varieties -- Projections of curves; 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.2020.07.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: For a given projective variety X, the high rank loci are the closures of the sets of points whose X -rank is higher than the generic one. We show examples of strict inclusion arising from two consecutive high rank loci. Our first example comes from looking at the Veronese surface of plane quartics. Although Piene had already shown an example in which X is a curve, we construct infinitely many curves in P 4 for which such strict inclusion appears. For space curves, we give two criteria to check whether the locus of points of maximum rank 3 is finite (possibly empty).