A Groebner basis for the determinantal ideal mod

Abstract: In an earlier paper [T. Košir, B.A. Sethuraman, Determinantal varieties over truncated polynomial rings, J. Pure Appl. Algebra 195 (2005) 75–95] we had begun a study of the components and dimensions of the spaces of th order jets of the classical determinantal varieties: these are the varieties obtained by considering generic () matrices over rings of the form , and for some fixed r, setting the coefficients of powers of t of all minors to zero. In this paper, we consider the case where , and provide a Groebner basis for the ideal which defines the tangent bundle to the classical determinantal variety. We use the results of these Groebner basis calculations to describe the components of the varieties where r is arbitrary. (The components of and were already described in the above cited paper.) [Copyright &y& Elsevier]