The parameter spaces for quadrics are reviewed. In addition, an explicit formula for the number of quadrics tangent to given linear subspaces is presented. 1. Schubert’s problem. 1.1. One century ago, in 1894, Schubert considered the following problem: Let P be a projective space. Assume there is given in P a finite number of linear subspaces in general position, say m1 hyperplanes, m2 codimension-2 planes, and in general, mi codimension-i planes. Then, how many quadrics in P are tangent to the given linear subspaces? In Schubert’s problem, the quadrics are assumed to be non-singular. Assume P = P(E) where E is a vector space of rank r. Then a non-singular quadric in P corresponds to a regular symmetric r×r matrix up to multiplication by a scalar. The symmetric matrices form a vector space of rank ( r+1 2 ) . Therefore, the set of non-zero symmetric matrices up to multiplication by a scalar is parametrized by a projective space of dimension N := ( r+1 2 ) −1. In this P , the matrices with non-zero determinant form an open subset U . By construction, the points of U correspond to the non-singular quadrics in P , that is, U is a parameter space for the set of non-singular quadrics in P . The set of quadrics that are tangent to a given linear subspace of P form, in the parameter space U , a hypersurface. Therefore, in Schubert’s problem it is natural to require that the number ∑ imi of given linear subspaces is equal to the dimension N of the parameter space. Then the quadrics tangent to the given linear subspaces correspond in the parameter space to the points in the intersection of N hypersurfaces. It could be hoped that the intersection is finite; Schubert’s problem is then to count the number of points in the intersection. To solve the counting problem by enumerative techniques, a closed (or complete) parameter space is needed. By construction, the space U is an open (dense) subset of P . A naive completion of U is then to take P as its closure. Clearly, the boundary points of U in P correspond to the singular quadrics in P . However, we cannot expect 1991 Mathematics Subject Classification: 14N10; 14M15. Supported in part by the Danish Natural Science Research Council, grant 11–7428. The paper is in final form and no version of it will be published elsewhere.