Prime Ideals and Three-generated Ideals with Large Regularity

Jason McCullough

doi:10.5802/crmath.544

Article de recherche - Algèbre

Prime Ideals and Three-generated Ideals with Large Regularity

Jason McCullough ¹

¹ Iowa State University, Department of Mathematics, Ames, IA, USA

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 251-255.

Résumé

Ananyan and Hochster proved the existence of a function $Φ (m, d)$ such that any graded ideal $I$ generated by $m$ forms of degree at most $d$ in a standard graded polynomial ring satisfies $reg (I) \leq Φ (m, d)$ . Relatedly, Caviglia et. al. proved the existence of a function $Ψ (e)$ such that any nondegenerate prime ideal $P$ of degree $e$ in a standard graded polynomial ring over an algebraically closed field satisfies $reg (P) \leq Ψ (deg (P))$ . We provide a construction showing that both $Φ (3, d)$ and $Ψ (e)$ must be at least doubly exponential in $d$ and $e$ , respectively. Previously known lower bounds were merely super-polynomial in both cases.

Reçu le : 2023-05-10
Révisé le : 2023-07-05
Accepté le : 2023-07-21
Publié le : 2024-05-02

DOI : 10.5802/crmath.544

Classification : 13D02, 13D05, 13P20

Affiliations des auteurs :

Jason McCullough ¹

¹ Iowa State University, Department of Mathematics, Ames, IA, USA

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Prime {Ideals} and {Three-generated} {Ideals} with {Large} {Regularity}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {251--255},
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     year = {2024},
     doi = {10.5802/crmath.544},
     language = {en},
}

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Jason McCullough. Prime Ideals and Three-generated Ideals with Large Regularity. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 251-255. doi : 10.5802/crmath.544. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.544/

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