THE EQUATIONS OF REES ALGEBRAS OF HEIGHT THREE GORENSTEIN IDEALS IN HYPERSURFACE RINGS

Abstract

We study the Rees algebra of a perfect Gorenstein ideal of codimension 3 in a hypersurface ring. We provide a minimal generating set for the defining ideal of these rings by introducing a modified Jacobian dual and applying a recursive algorithm. Once the defining equations are known, we explore properties of these Rees algebras such as Cohen–Macaulayness and Castelnuovo–Mumford regularity.