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 $K[x_1,\dots ,x_n]$. 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.

Minor changes. This article is part of the special volume for Women in Commutative Algebra, Proceedings of the 2019 WICA Workshop