The Structure of an Even Liaison Class

We describe a structure called the Lazarsfeld-Rao property for even liaison classes in projective space. This property holds for many even liaison classes of curves in <!-- MATH ${{\mathbf{P}}^3}$ --> . We give a procedure for showing that an even liaison class in codimension possesses this property, and we prove it for a family of even liaison classes in codimension in any <!-- MATH ${{\mathbf{P}}^n},\;n \geqslant 3$ --> . However, we conjecture that it in fact holds for every even liaison class in codimension , so we want to give consequences for an even liaison class that possesses this property.