On the Hilbert depth of the Hilbert function of a finitely generated graded module

• Published in: Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică Vol. 33; no. 1; pp. 49 - 64
• Main Authors: Bălănescu, Silviu, Cimpoeaş, Mircea
• Format: Journal Article
• Language: English
• Published: Constanta Sciendo 01.03.2025; De Gruyter Poland
• Subjects: Graded module; Hilbert depth; Hypergeometric function; Monomial ideal; Primary 13C15, 13P10, 13F20; Secondary 05A18, 06A07
• ISSN: 1224-1784; 1844-0835
• DOI: 10.2478/auom-2025-0003

Let be a field, a standard graded -algebra and a finitely generated graded -module. Inspired by our previous works, see [2] and [3], we study the invariant called Hilbert depth of h , that is where (−) is the Hilbert function of , and we prove basic results regard it. Using the theory of hypergeometric functions, we prove that hdepth( ) = , where = , . . . , ]. We show that hdepth( ) = , if = ( , . . . , ) ⊂ is a complete intersection monomial ideal with deg(f ) ≥ 2 for all 1 ≤ ≤ . Also, we show that hdepth( ) ≥ hdepth( ) for any finitely generated graded -module , where = ⊗ [x ].