Geometric conditions for strict submultiplicativity of rank and border rank

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  • Edoardo Ballico
  • Alessandra Bernardi
  • Gesmundo, Fulvio
  • Alessandro Oneto
  • Emanuele Ventura

The X-rank of a point p in projective space is the minimal number of points of an algebraic variety X whose linear span contains p. This notion is naturally submultiplicative under tensor product. We study geometric conditions that guarantee strict submultiplicativity. We prove that in the case of points of rank two, strict submultiplicativity is entirely characterized in terms of the trisecant lines to the variety. Moreover, we focus on the case of curves: we prove that for curves embedded in an even-dimensional projective space, there are always points for which strict submultiplicativity occurs, with the only exception of rational normal curves.

TidsskriftAnnali di Matematica Pura ed Applicata
Antal sider24
StatusE-pub ahead of print - 2020

ID: 242663056