Extensions of the Multiplicity Conjecture

2005/05/11 by Juan Migliore, Migliore, Juan, Uwe Nagel +3
Mathematics · #13C40 #13D02 #13H15 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13C40 #msc:13D02 #msc:13H15

paper · pdf · doi:10.48550/arxiv.math/0505229

22 pages

arxiv created 2005/05/11 · arxiv updated 2009/12/01

Abstract

The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded k-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several directions. We discuss when these bounds are sharp, find a sharp lower bound in case of not necessarily arithmetically Cohen-Macaulay one-dimensional schemes of 3-space, and we propose an upper bound for finitely generated graded torsion modules. We establish this bound for torsion modules whose codimension is at most two.

Related

• The Multiplicity Conjecture in low codimensions
• A note on the multiplicity of determinantal ideals
• On the Upper bound of the Multiplicity Conjecture
• An upper bound for the multiplicity and Wilf's conjecture for one-dimensional Cohen-Macaulay rings
• A multiplicity bound for graded rings and a criterion for the Cohen-Macaulay property