Let d_{ k,n} and #_{ k,n} denote the dimension and the degree of the Grassmannian G_{ k,n} of k-planes in projective n-space, respectively. For each k between 1 and n-2 there are 2^{ d_{ k,n}} \cdot #_{ k,n} (a priori complex) k-planes in P^n tangent to d_{ k,n} general quadratic hypersurfaces in P^n. We show that this class of enumerative problem is fully real, i.e., for each k between 1 and n-2 there exists a configuration of d_{ k,n} real quadrics in (affine) real space R^n so that all the mutually tangent k-flats are real.
Categories: math.AG math.CO