ADJACENT INTEGRALLY CLOSED IDEALS IN DIMENSION 2

Let I be an m-primary integrally. closed ideal in a 2-dimensional regular local ring R. Zariski proved that I can be uniquely factored into a product of simple integrally closed ideals, and Lipman later proved that the Hilbert function HI(n) = lambda(R/I(n)) of I is a polynomial for all n greater-than-or-equal-to 1. By using these results with many others, we study various properties of adjacent integrally closed ideals in 2-dimensional regular local rings. In particular, multiplicities, factorizations, minimal reductions, and Rees valuations of adjacent integrally closed ideals are studied.