Ovoid (polar space)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the field of combinatorics, a polar space of rank n (n 3), or projective index n 1, consists of a set P, conventionally the set of points, together with certain subsets of P, called subspaces, that satisfy these axioms : Every subspace, together with its own subspaces, is isomorphic with a partial geometry PG(d,q) with 1 d (n 1) and q a prime power. By definition, for each subspace the corresponding d is its dimension. The intersection of two subspaces is always a subspace. For each point p not in a subspace A of dimension of n 1, there is a unique subspace B of dimension n 1 such that A B is (n 2)-dimensional. The points in A B are exactly the points of A that are in a common subspace of dimension 1 with p. There are at least two disjoint subspaces of dimension n 1. A polar space of rank two is a generalized quadrangle.... Mehr