The Briançon-Skoda number of analytic irreducible planar curves

Abstract

The Briançon-Skoda number of a ring R is defined as the smallest integer k, such that for any ideal I ⊂ R and l ≥ 1, the integral closure of I k+l−1 is contained in I l . We compute the Briançon-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.

Global effective versions of the Briançon–Skoda–Huneke theorem

“…In fact, in view of [31,Section 2] and the proof below one finds that Theorem B holds with μ 0 = a p in this case. From [18,Proposition 4.16] we know that ν L ≤ reg X − 2 = p − 2.…”