Asymptotics of degrees and ED degrees of Segre products

Giorgio Ottaviani, Luca Sodomaco*, Emanuele Ventura

*Tämän työn vastaava kirjoittaja

Tutkimustuotos: LehtiartikkeliArticleScientificvertaisarvioitu

3 Sitaatiot (Scopus)
21 Lataukset (Pure)

Abstrakti

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.

AlkuperäiskieliEnglanti
Artikkeli102242
Sivumäärä36
JulkaisuAdvances in Applied Mathematics
Vuosikerta130
DOI - pysyväislinkit
TilaJulkaistu - syyskuuta 2021
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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