A Survey on the Eisenbud-Green-Harris Conjecture

Abstract

The Eisenbud-Green-Harris (EGH) conjecture offers a generalization of the famous Macaulay's theorem about the Hilbert functions of homogeneous ideals in a polynomial ring K[x 1 , . . . , x n ]. In this survey paper, we provide a good compilation of results on the EGH conjecture that have been obtained so far. We discuss these results in terms of their approaches.