The Eisenbud-Green-Harris conjecture for fast-growing degree sequences

2020/07/30 by Giulio Caviglia, Caviglia, Giulio, Alessandro De Stefani +1
Mathematics · #13A02 #13A15 #13D02 #13P10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2007.15467

openalex publication_date 2020/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a standard graded polynomial ring over a field, and I be a homogeneous ideal that contains a regular sequence of degrees d₁,…,d_n. We prove the Eisenbud-Green-Harris conjecture when the forms of the regular sequence satisfy d_i \geqslant ∑_j=1^i-1(d_j-1), improving a result obtained in 2008 by the first author and Maclagan. Except for the sporadic case of a regular sequence of five quadrics, recently proved by Güntürkün and Hochster, the results of this article recover all known cases of the conjecture where only the degrees of the regular sequence are fixed, and include several additional ones.

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