2012/05/14 by P. H. Lima, Lima, P. H., V. H. Jorge Pérez +2
Computer Science · Mathematics · #13D40 #13H15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.AC #math.AG #math.RA #msc:13D40 #msc:13H15
paper · pdf · doi:10.48550/arxiv.1205.3148
arxiv created 2012/05/14 · openalex publication_date 2012/05/14 · arxiv updated 2012/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (A, \mathfrakm) be a Noetherian local ring and \mathfrakF=(In)n≥ 0 a filtration. In this paper, we study the Gorenstein properties of the fiber cone F(\mathfrakF), where \mathfrakF is a Hilbert filtration. Suppose that F(\mathfrakF) and G(\mathfrakF) are Cohen-Macaulay. If in addition, the associated graded ring G(\mathfrakF) is Gorenstein; similarly to the I-adic case, we obtain a necessary and sufficient condition, in terms of lengths and minimal number of generators of ideals, for Gorensteiness of the fiber cone. Moreover, we find a description of the canonical module of F(\mathfrakF) and show that even in the Hilbert filtration case, the multiplicity of the canonical module of the fiber cone is upper bounded by multiplicity of the canonical modules of the associated graded ring.