Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Real k-Flats Tangent to Quadrics in Rn

Frank Sottile and Thorsten Theobald
Proceedings of the American Mathematical Society
Vol. 133, No. 10 (Oct., 2005), pp. 2835-2844
Stable URL: http://www.jstor.org/stable/4097896
Page Count: 10
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Real k-Flats Tangent to Quadrics in Rn
Preview not available

Abstract

Let $d_{k, n}$ and $\#_{k, n}$ denote the dimension and the degree of the Grassmannian $\mathbb{G}_{k, n}$, respectively. For each $1 \leq k \leq n - 2$ there are $2^{d_{k, n}} \cdot \#_{k, n}$ (a priori complex) k-planes in Pn tangent to $d_{k, n}$ general quadratic hypersurfaces in Pn. We show that this class of enumerative problems is fully real, i.e., for $1 \leq k \leq n - 2$ there exists a configuration of $d_{k, n}$ real quadrics in (affine) real space Rn so that all the mutually tangent k-flats are real.

Page Thumbnails

  • Thumbnail: Page 
2835
    2835
  • Thumbnail: Page 
2836
    2836
  • Thumbnail: Page 
2837
    2837
  • Thumbnail: Page 
2838
    2838
  • Thumbnail: Page 
2839
    2839
  • Thumbnail: Page 
2840
    2840
  • Thumbnail: Page 
2841
    2841
  • Thumbnail: Page 
2842
    2842
  • Thumbnail: Page 
2843
    2843
  • Thumbnail: Page 
2844
    2844