Effective computation of base points of ideals in two-dimensional local rings

TL;DR

This paper presents a method to compute the base points of ideals in two-dimensional local rings by deriving a minimal log-resolution from the resolutions of the ideal's generators, simplifying the process.

Contribution

It introduces a novel approach to obtain the minimal log-resolution of an ideal directly from the resolutions of its generators in smooth complex surfaces.

Findings

Provides a procedure to compute base points efficiently.

Connects the resolutions of generators to the ideal's overall resolution.

Simplifies the process of resolving ideals in complex surfaces.

Abstract

In this work we describe a minimal log-resolution of an ideal in a smooth complex surface from the minimal log-resolution of its generators.