An improved Multiplicity Conjecture for codimension three Gorenstein   algebras
  The Multiplicity Conjecture is a deep problem relating the multiplicity (or degree) of a Cohen-Macaulay standard graded algebra with certain extremal graded Betti numbers in its minimal free resolution. In the case of level algebras of codimension three, Zanello has proposed a stronger conjecture. We prove this conjecture for the case of codimension three graded Gorenstein algebras. 
Juan C. Migliore, Uwe Nagel, Fabrizio Zanello