Rees algebras of truncations of complete intersections

Abstract In this paper we describe the defining equations of the Rees algebra and the special fiber ring of a truncation I of a complete intersection ideal in a polynomial ring over a field with homogeneous maximal ideal m . To describe explicitly the Rees algebra R ( I ) in terms of generators and relations we map another Rees ring R ( M ) onto it, where M is the direct sum of powers of m . We compute a Grobner basis of the ideal defining R ( M ) . It turns out that the normal domain R ( M ) is a Koszul algebra and from this we deduce that in many instances R ( I ) is a Koszul algebra as well.