Finitely supported ⁎-simple complete ideals in a regular local ring

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

rigid resolution of a finitely generated module over a regular local ring

On the value-semigroup of a simple complete ideal in a two-dimensional regular local ring

Let R be a two-dimensional regular local ring with maximal ideal m, and let ℘ be a simple complete m-primary ideal which is residually rational. Let R0 := R $ R1 $ · · · $ Rr be the quadratic sequence associated to ℘, let Γ℘ be the value-semigroup associated to ℘, and let (ej(℘))0≤j≤r be the multiplicity sequence of ℘. We associate to ℘ a sequence (γi(℘))0≤i≤g of natural integers which we call ...

Complete Ideals in 2-dimensional Regular Local Rings

The objective of these notes is to present a few important results about complete ideals in 2–dimensional regular local rings. The fundamental theorems about such ideals are due to Zariski found in appendix 5 of [26]. These results were proved by Zariski in [27] for 2dimensional polynomial rings over an algebraically closed field of characteristic zero and rings of holomorphic functions. Zarisk...

The Poincaré Series of Multiplier Ideals of a Simple Complete Ideal in a Local Ring of a Smooth Surface

For a simple complete ideal ℘ of a local ring at a closed point on a smooth complex algebraic surface, we introduce an algebraic object, named Poincaré series P℘, that gathers in an unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to ℘. This paper is devoted to prove that P℘ is a rational function giving an explicit...