Chains of integrally closed ideals

Abstract

Let $(A,\mathfrak{m})$ be an excellent normal local ring with algebraically closed residue class field. Given integrally closed $\mathfrak{m}$-primary ideals $I\supset J$, we show that there is a composition series between $I$ and $J$, by integrally closed ideals only. Also we show that any given integrally closed $\fm$-primary ideal $I$, the family of integrally closed ideals $J\subset I,l_A(I/J)=1$ forms an algebraic variety with dimension $\dim A-1$.

6 pages, to appear in contemporary math