Some cases of the Eisenbud-Green-Harris conjecture

Details Some cases of the Eisenbud-Green-Harris conjecture Some cases of the Eisenbud-Green-Harris conjecture

2006-11-16

arxiv.org/abs/math/0611488v1

Mathematics

Commutative Algebra

8 pages

Scientific paper

The Eisenbud-Green-Harris conjecture states that a homogeneous ideal in k[x_1,...,x_n] containing a homogeneous regular sequence f_1,...,f_n with deg(f_i)=a_i has the same Hilbert function as an ideal containing x_i^{a_i} for 1 \leq i \leq n. In this paper we prove the Eisenbud-Green-Harris conjecture when a_j> sum_{i=1}^{j-1} (a_i-1) for all j>1. This result was independently obtained by the two authors.

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