Symmetric and Rees algebras of Koszul cycles and their Gr�bner bases

Abstract

In this paper we study the symmetric algebra S(Ei) and Rees algebra R(Ei) of the modules Ei of i-cycles of the Koszul complex associated with the sequence of indeterminates \({{x_1,\ldots, x_n}}\) of a polynomial ring \({{K[x_1,\ldots, x_n]}}\). For i=2 and i=n−2 we show that \({{x_1,\ldots, x_n}}\) is a d-sequence on S(Ei) and R(Ei) and we determine Grobner bases and Sagbi bases related to these algebras.