The Multiplicity Conjecture in low codimensions

Juan C. Migliore , Uwe Nagel , Tim Römer

MSC 2000

13D02 Syzygies and resolutions

13C40 Linkage, complete intersections and determinantal ideals

Abstract
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.