Symmetric powers of complete modules over a two-dimensional regular local ring

Abstract

Let (R, m) be a two-dimensional regular local ring with infinite residue field. For a finitely generated, torsion-free R-module A, write A_n for the n^th symmetric power of A, mod torsion. We study the modules A_n , n ≥ 1, when A is complete (i.e., integrally closed). In particular, we show that B·A = A₂ , for any minimal reduction B⊆A and that the ring ⊕_n≥1 A_n is Cohen-Macaulay.