Degrees of Kalman varieties of tensors
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2023-01-01
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Language
en
Pages
25
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Journal of Symbolic Computation, Volume 114, pp. 74-98
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.Description
Funding Information: The idea of this project was conceived during Shahidi's postdoc at Università di Firenze. We thank Giorgio Ottaviani for very useful discussions and encouragement. We thank Jan Draisma for explaining to us a way of deriving the equations in Example 41 . The first author thanks Dr. Alireza Firoozfar and Dr. Mohsen Afsharchi for their support. The second author is partially supported by the Academy of Finland Grant 323416 . During most of the preparation of the manuscript, the third author was a postdoc at Universität Bern, supported by Vici Grant 639.033.514 of Jan Draisma from the Netherlands Organisation for Scientific Research . We thank two anonymous referees for their useful comments and questions that also helped to improve the presentation. Publisher Copyright: © 2022 The Author(s)
Keywords
Asymptotics, Generating function, Kalman variety, Singular vector tuples, Tensors
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Citation
Shahidi, Z, Sodomaco, L & Ventura, E 2023, ' Degrees of Kalman varieties of tensors ', Journal of Symbolic Computation, vol. 114, pp. 74-98 . https://doi.org/10.1016/j.jsc.2022.04.016