Some cases of the Eisenbud-Green-Harris conjecture
Giulio Caviglia, Diane Maclagan
Abstract
The Eisenbud-Green-Harris conjecture states that a homogeneous ideal in k[x1,...,xn] containing a homogeneous regular sequence f1,...,fn with deg(fi)=ai has the same Hilbert function as an ideal containing xiai for 1 ≤ i ≤ n. In this paper we prove the Eisenbud-Green-Harris conjecture when aj> sumi=1j-1 (ai-1) for all j>1. This result was independently obtained by the two authors.
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