Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700 ; Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
Abstract:
Let be an -dimensional vector space over an algebraically closed field . Define to be the least positive integer for which there exists a family of -dimensional subspaces of such that every -dimensional subspace of has at least one complement among the 's. Using algebraic geometry we prove that .