Mathematical Research Letters

Volume 12 (2005)

Number 5

The multiplicity conjecture in low codimensions

Pages: 731 – 748



Juan Migliore (University of Notre Dame)

Uwe Nagel (University of Kentucky)

Tim Römer (Universität Osnabrück)


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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