Asymptotics of degrees and ED degrees of Segre products
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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2021-09
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Mcode
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Language
en
Pages
36
Series
Advances in Applied Mathematics, Volume 130
Abstract
Two fundamental invariants attached to a projective variety are its classical algebraic degree and its Euclidean Distance degree (ED degree). In this paper, we study the asymptotic behavior of these two degrees of some Segre products and their dual varieties. We analyze the asymptotics of degrees of (hypercubical) hyperdeterminants, the dual hypersurfaces to Segre varieties. We offer an alternative viewpoint on the stabilization of the ED degree of some Segre varieties. Although this phenomenon was incidentally known from Friedland-Ottaviani's formula expressing the number of singular vector tuples of a general tensor, our approach provides a geometric explanation. Finally, we establish the stabilization of the degree of the dual variety of a Segre product X×Qn, where X is a projective variety and Qn⊂Pn+1 is a smooth quadric hypersurface.Description
Funding Information: We thank Jay Pantone for very useful conversations. We thank the referees for useful comments. The first two authors are members of INDAM-GNSAGA. The third author would like to thank The Department of Mathematics of Universit? di Firenze, where this project started in June 2018, for the warm hospitality and financial support. The first author is supported by the H2020-MSCA-ITN-2018 project POEMA. The second author is partially supported by the Academy of Finland Grant 323416. The third author is supported by Vici Grant 639.033.514 of Jan Draisma from the Netherlands Organisation for Scientific Research. Publisher Copyright: © 2021 The Author(s)
Keywords
Asymptotics, Dual varieties, ED degrees, Hyperdeterminants, Segre products, Tensors
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Citation
Ottaviani, G, Sodomaco, L & Ventura, E 2021, ' Asymptotics of degrees and ED degrees of Segre products ', Advances in Applied Mathematics, vol. 130, 102242 . https://doi.org/10.1016/j.aam.2021.102242
