The regularity index, Hilbert function of fat points and the embedding

2023/10/16 by Phan Van Thiên, Van Thien, Phan
Mathematics · #13D40 #A.0 #Advanced Banach Space Theory #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Point processes and geometric inequalities #Primary 14C20

paper · pdf · doi:10.48550/arxiv.2310.10212

openalex publication_date 2023/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let m ≥ n, ϕ_n,m: \mathbb Pⁿ → \mathbb P^m, ϕ_n,m(a₁, …, a_n)=(a₁, …, a_n, 0, …, 0), be the embedding, Z=m₁P₁+⋯+m_sP_s be fat points in \mathbb Pⁿ and ϕ_n,m(Z)=m₁ϕ_n,m(P₁)+⋯+m_sϕ_n,m(P_s) be fat points in \mathbb P^m. We show the relation between the regularity index, Hilbert function of the fat points Z and the regularity index, Hilbert function of the fat points ϕ_n,m(Z).

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