On the Hilbert functions of the elements of the Terracini loci of the Veronese varieties

• Ballico, Edoardo ^[1]
  1. [1] University of Trento

     University of Trento

     Trento, Italia

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 1, 2026, págs. 149-160
• Idioma: inglés
• DOI: 10.1007/s13348-024-00462-8
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study the Hilbert functions (often the most extreme ones) of the finite subsets S\subset {\mathbb {P}}^n which are Terracini for the order d Veronese embedding of {\mathbb {P}}^n, i.e. S spans {\mathbb {P}}^n, the fat scheme 2S:= \cup _{p\in S}2p is contained in a degree d hypersurface and 2S is defective in degree d. Call {\mathbb {T}}(n,d;x) the set of all such sets S with \#S=x. We compute or bound the minimum and the maximum of the first degree of a hypersurface containing S (resp. 2S) and the index of regularity of S (resp. 2S) when S varies in {\mathbb {T}}(n,d;x). We give stronger results on the Hilbert function of S and 2S for S in some defined subset of {\mathbb {T}}(n,d;x).

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