# On finite determinacy of complete intersection singularities

## TL;DR

This paper proves that real or complex analytic complete intersection germs are equisingular with algebraic sets defined by sufficiently long truncations of their defining equations, using an elementary combinatorial proof.

## Contribution

It provides a new elementary combinatorial proof of finite determinacy for complete intersection singularities.

## Key findings

- Complete intersection germs are equisingular with algebraic sets from truncated equations.
- The proof is elementary and combinatorial.
- Finite determinacy holds for these singularities.

## Abstract

We give an elementary combinatorial proof of the following fact: Every real or complex analytic complete intersection germ X is equisingular -- in the sense of the Hilbert-Samuel function -- with a germ of an algebraic set defined by sufficiently long truncations of the defining equations of X.