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Journal Article

# 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

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## 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.

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