Real k k -flats tangent to quadrics in R n mathbb {R}^n Conference Paper

Let d k , n d_{k,n} and # k , n #_{k,n} denote the dimension and the degree of the Grassmannian G k , n mathbb {G}_{k,n} , respectively. For each 1 k n 2 1 le k le n-2 there are 2 d k , n # k , n 2^{d_{k,n}} cdot #_{k,n} (a priori complex) k k -planes in P n mathbb {P}^n tangent to d k , n d_{k,n} general quadratic hypersurfaces in P n mathbb {P}^n . We show that this class of enumerative problems is fully real, i.e., for 1 k n 2 1 le k le n-2 there exists a configuration of d k , n