Secant dimensions of low-dimensional homogeneous varieties

@article{Baur2007SecantDO,
  title={Secant dimensions of low-dimensional homogeneous varieties},
  author={K. Baur and J. Draisma},
  journal={Algebra & Number Theory},
  year={2007}
}
  • K. Baur, J. Draisma
  • Published 2007
  • Mathematics
  • Algebra & Number Theory
  • We completely describe the higher secant dimensions of all connected homogeneous projective varieties of dimension at most 3, in all possible equivariant embeddings. In particular, we calculate these dimensions for all Segre–Veronese embeddings of P1 × P1, P1 × P1 × P1, and P2 × P1, as well as for the flag variety F of incident point-line pairs in P2. For P2 × P1 and F the results are new, while the proofs for the other two varieties are more compact than existing proofs. Our main tool is the… CONTINUE READING
    20 Citations
    On the dimensions of secant varieties of Segre-Veronese varieties
    • 33
    • Highly Influenced
    • PDF
    Secant Varieties of Segre–Veronese Varieties ℙ m × ℙ n Embedded by O(1, 2)
    • 23
    • PDF

    References

    SHOWING 1-10 OF 15 REFERENCES
    A tropical approach to secant dimensions
    • 75
    • PDF
    Segre-Veronese embeddings of P1xP1xP1 and their secant varieties .
    • 24
    • Highly Influential
    Tropical Secant Varieties of Linear Spaces
    • M. Develin
    • Mathematics, Computer Science
    • Discret. Comput. Geom.
    • 2006
    • 17
    • PDF
    Combinatorial secant varieties
    • 70
    • PDF
    On the Alexander–Hirschowitz theorem
    • 116
    • PDF
    Higher secant varieties of Segre-Veronese varieties
    • 67
    • PDF
    Polynomial interpolation in several variables
    • 562
    • PDF