The Briancon-Skoda number of analytic irreducible planar curves

TL;DR

This paper computes the Briancon-Skoda number for analytic irreducible planar curves using Puiseux characteristics, revealing its close relation to the Milnor number, thus advancing understanding of singularity invariants.

Contribution

It provides an explicit formula for the Briancon-Skoda number of irreducible planar curves based on Puiseux data, connecting algebraic and topological invariants.

Findings

Briancon-Skoda number expressed via Puiseux characteristics

Number closely related to the Milnor number

Advances understanding of singularity invariants

Abstract

The Briancon-Skoda number of a ring R is defined as the smallest integer k, such that for any ideal I\subset R and r\geq 1, the integral closure of I^{k+r-1} is contained in I^r. We compute the Briancon-Skoda number of the local ring of any analytic irreducible planar curve in terms of its Puiseux characteristics. It turns out that this number is closely related to the Milnor number.