ON THE EISENBUD-GREEN-HARRIS CONJECTURE

摘要

It has been conjectured by Eisenbud, Green and Harris that if I is a homogeneous ideal in k[x(1), ..., x(n)] containing a regular sequence f(1), ..., f(n) of degrees deg(f(i)) = a(i), where 2 <= a(1) <= ... <= a(n), then there is a homogeneous ideal J containing x(1)(a1), ..., x(n)(an) with the same Hilbert function. In this paper we prove the Eisenbud-Green-Harris Conjecture when f(i) splits into linear factors for all i.