Some cases of the Eisenbud-Green-Harris conjecture

2006/11/16 by Giulio Caviglia, Diane Maclagan, Caviglia, Giulio +1
Computer Science · Mathematics · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC

paper · pdf · doi:10.48550/arxiv.math/0611488

8 pages

arxiv created 2006/11/16 · openalex publication_date 2006/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Eisenbud-Green-Harris conjecture states that a homogeneous ideal in k[x₁,...,x_n] containing a homogeneous regular sequence f₁,...,f_n with deg(f_i)=a_i has the same Hilbert function as an ideal containing x_i^a_i for 1 ≤ i ≤ 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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