2012/05/24 by Juan Elías, Elias, J., Maria Evelina Rossi +3
Computer Science · Mathematics · #13H10 #13H15 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1205.5357
openalex publication_date 2012/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hilbert function of standard graded algebras are well understood by Macaulay's theorem and very little is known in the local case, even if we assume that the local ring is a complete intersection. An extension to the power series ring R of the theory of Gröbner bases (w.r.t. local degree orderings) enable us to characterize the Hilbert function of one dimensional quadratic complete intersections A=R/I, and we give a structure theorem of the minimal system of generators of I in terms of the Hilbert function. We find several restrictions for the Hilbert function of A in the case that I is a complete intersection of type (2,b). Conditions for the Cohen-Macaulyness of the associated graded ring of A are given.