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arXiv · 2408.03477

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

Mario Maican
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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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Mario Maican. 2024-08-06. The Relevant Domain of the Hilbert Function of a Finite Multiprojective Scheme. https://arxiv.org/abs/2408.03477

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