Extensions of the Multiplicity Conjecture

Details Extensions of the Multiplicity Conjecture Extensions of the Multiplicity Conjecture

2005-05-11

arxiv.org/abs/math/0505229v1

Mathematics

Commutative Algebra

22 pages

Scientific paper

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.

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