The Relevant Domain of the Hilbert Function of a Finite Multiprojective Scheme

2024/08/06 by Mario Maican, Maican, Mario · 1 citation
Computer Science · Mathematics · #13D40 #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2408.03477

openalex publication_date 2024/08/06 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

Let X be a zero-dimensional scheme contained in a multiprojective space. Let s_i be the length of the projection of X onto the i-th component of the multiprojective space. A result of Van Tuyl states that the Hilbert function of X, in the case when X is reduced, is completely determined by its restriction to the product of the intervals [0, s_i - 1]. We prove that the same is also true for non-reduced schemes X.

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