Milnor and Tjurina numbers for an isolated complete intersection singularity

TL;DR

This paper establishes a bound on the Milnor number of an isolated complete intersection singularity based solely on its Tjurina number and dimension, using advanced algebraic methods.

Contribution

It introduces a new bound relating Milnor and Tjurina numbers for singularities, utilizing the A$ ext{ extit{m}}$AC method.

Findings

Bound depends only on Tjurina number and dimension

Uses A$ ext{ extit{m}}$AC technique for proof

Bound is purely existential

Abstract

This paper aims to prove that given a isolated complete intersection singularity, the Milnor number will be bounded by a bound depending only on Tjurina number and dimension of the singularity. The proof uses A$\mathfrak{m}$AC (introduced in arXiv:2204.05594) and as with such methods, the bound is purely existential.