Asymptotics of degrees and ED degrees of Segre products

Giorgio Ottaviani, Luca Sodomaco*, Emanuele Ventura

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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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.

Original languageEnglish
Article number102242
Number of pages36
JournalAdvances in Applied Mathematics
Volume130
DOIs
Publication statusPublished - Sep 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Asymptotics
  • Dual varieties
  • ED degrees
  • Hyperdeterminants
  • Segre products
  • Tensors

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