An upper bound for the multiplicity and Wilf's conjecture for one-dimensional Cohen-Macaulay rings

2025/02/25 by D'Anna, Marco, Moscariello, Alessio
#13H10 #13H15 #20M14 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.17989

Abstract

In this work we provide an upper bound for the multiplicity of a one-dimensional Cohen-Macaulay ring (under certain conditions), describe the rings attaining the equality for this bound, and outline a connection with Wilf's conjecture for numerical semigroup rings. Then we prove the analogue of Wilf's conjecture for almost Gorenstein rings.

Related

• A multiplicity bound for graded rings and a criterion for the Cohen-Macaulay property
• Conditions of multiplicity and applications for almost Gorenstein graded rings
• Extensions of the Multiplicity Conjecture
• Multiplicity bounds in prime characteristic
• Upper bound of multiplicity in Cohen-Macaulay rings of prime characteristic