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On the relevant domain of the Hilbert function of a finite multiprojective scheme

Part of: Projective and enumerative geometry Commutative algebra: Homological methods

Published online by Cambridge University Press:  03 November 2025

Mario Maican
Mario Maican*
Affiliation:
Institute of Mathematics of the Romanian Academy , Bucharest, Romania
*
e-mail: maican@imar.ro
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Abstract

Let X be a zero-dimensional reduced subscheme of a multiprojective space $\mathbb {V} $. Let $s_i$ be the length of the projection of X onto the ith component of $\mathbb {V}$. A result of Van Tuyl states that the Hilbert function of X is completely determined by its restriction to the product of the intervals $[0, s_i - 1]$. We extend this result to arbitrary zero-dimensional subschemes of $\mathbb {V}$.

Keywords

Hilbert functionzero-dimensional schememultiprojective scheme

MSC classification

Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 14N05: Projective techniques

Information

Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 31
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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