Geometric conditions for strict submultiplicativity of rank and border rank
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
---|---|
Journal | Annali di Matematica Pura ed Applicata |
Volume | 200 |
Issue number | 1 |
Pages (from-to) | 187-210 |
ISSN | 0373-3114 |
DOIs | |
Publication status | Published - 2021 |
- Border rank, Rank, Secant variety, Segre product, Tensor product
Research areas
Links
- https://arxiv.org/pdf/1909.03811.pdf
Accepted author manuscript
ID: 242663056