Rees algebras and Koszul homology

AbstractThis paper deals with properties of a Cohen-Macaulay ideal I in a regular local ring R. We consider two main kinds of ideals: strongly Cohen-Macaulay ideals and ideals with sliding depth. One of our aims is to sharpen their differences. We also examine certain kinds of normal ideals and consider ways of determining the divisor class group and the canonical module of its Rees algebra. We show that the divisor class group of R(I) is a finitely generated free abelian group. The main results of this work are certain numerical constraints that are shown to exist on the projective resolutions of graded ideals with Cohen-Macaulay Koszul homology