Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

On multigraded resolutions

Winfried Brunsa1 and Jürgen Herzoga2

a1 Universität Osnabrück, Standort Vechta. D-49364 Vechta, Germany

a2 Universität Essen, FB Mathematik und Informatik, D-45117 Essen, Germany

This paper was initiated by a question of Eisenbud who asked whether the entries of the matrices in a minimal free resolution of a monomial ideal (which, after a suitable choice of bases, are monomials) divide the least common multiple of the generators of the ideal. We will see that this is indeed the case, and prove it by lifting the multigraded resolution of an ideal, or more generally of a multigraded module, keeping track of how the shifts ‘deform’' in such a lifting; see Theorem 2·1 and Corollary 2·2.

(Received April 28 1994)

(Revised August 15 1994)