Degrees of Kalman varieties of tensors. (January 2023)

• Record Type: Journal Article
• Authors: Shahidi, Zahra; Sodomaco, Luca; Ventura, Emanuele
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 74
• Page End: 98
• Publication Date: 2023-01
• Subjects: 14N07 -- 14N05 -- 14N10 -- 15A69 -- 15A18; Tensors -- Singular vector tuples -- Kalman variety -- Generating function -- Asymptotics; 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.2022.04.016
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Kalman varieties of tensors are algebraic varieties consisting of tensors whose singular vector k -tuples lay on prescribed subvarieties. They were first studied by Ottaviani and Sturmfels in the context of matrices. We extend recent results of Ottaviani and the first author to the partially symmetric setting. We describe a generating function whose coefficients are the degrees of these varieties and we analyze its asymptotics, providing analytic results à la Zeilberger and Pantone. We emphasize the special role of isotropic vectors in the spectral theory of tensors and describe the totally isotropic Kalman variety as a dual variety.