Chains of integrally closed ideals

الأصل · EN

Let (A, m) be an excellent normal local ring with algebraically closed residue class field. Given integrally closed m-primary ideals I⊃ 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 -primary ideal I, the family of integrally closed ideals J⊂ I, lₐ(I/J)=1 forms an algebraic variety with dimension A -1.