Recent intrinsic characterizations of ovoids and elliptic quadrics in PG(3,K)

Abstract

Let PG(3,K) be a pappian projective space. There has been much study of ovoids and elliptic quadrics in PG(3,K) as well as subset with various properties which characterize them. A more difficult question is to characterize such subsets in an intrinsic way, i.e. starting with an abstract set which is not necessarily embeddable in any PG(3,K). Starting with the celebrated Buekenhout's article [7], this paper surveys some important known approaches and results, obtained after 1973, on this intrinsic characterizations of ovoids and elliptic quadrics to bringing up to date references and results.