The range of all regularities for polynomial ideals with a given Hilbert function
| Autor: | Francesca Cioffi |
|---|---|
| Přispěvatelé: | Cioffi, Francesca |
| Rok vydání: | 2021 |
| Předmět: |
Castelnuovo-Mumford regularity
Hilbert function Minimal function Strongly stable ideal Pure mathematics Polynomial Polynomial ring Field (mathematics) Interval (mathematics) Commutative Algebra (math.AC) 01 natural sciences Constructive symbols.namesake Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics Ideal (ring theory) 0101 mathematics Mathematics Hilbert series and Hilbert polynomial Algebra and Number Theory Mathematics::Commutative Algebra High Energy Physics::Phenomenology 010102 general mathematics Mathematics - Commutative Algebra Range (mathematics) 13P99 14Q99 68W30 11Y55 symbols 010307 mathematical physics |
| Zdroj: | Journal of Algebra. 566:435-442 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2020.10.003 |
| Popis: | Given the Hilbert function $u$ of a closed subscheme of a projective space over an infinite field $K$, let $m_u$ and $M_u$ be, respectively, the minimum and the maximum among all the Castelnuovo-Mumford regularities of schemes with Hilbert function $u$. I show that, for every integer $m$ such that $m_u \leq m \leq M_u$, there exists a scheme with Hilbert function $u$ and Castelnuovo-Mumford regularity $m$. As a consequence, the analogous algebraic result for an O-sequence $f$ and homogeneous polynomial ideals over $K$ with Hilbert function $f$ holds too. Although this result does not need any explicit computation, I also describe how to compute a scheme with the above requested properties. Precisely, I give a method to construct a strongly stable ideal defining such a scheme. Comment: 15 pages. Comments and suggestions are welcome |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect