The Multiplicity Conjecture in low codimensions

Details The Multiplicity Conjecture in low codimensions The Multiplicity Conjecture in low codimensions

2004-10-22

arxiv.org/abs/math/0410497v1

Mathematics

Commutative Algebra

17 pages

Scientific paper

We establish the multiplicity conjecture of Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen-Macaulay algebras over a field, for codimension two algebras and for Gorenstein algebras of codimension three. In fact, we prove stronger bounds than the conjectured ones allowing us to characterize the extremal cases. This may be seen as a converse to the multiplicity formula of Huneke and Miller that inspired the conjectural bounds.

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