A new proof of monomialisation from 3-folds to surfaces

TL;DR

This paper presents a novel proof of monomialisation for morphisms from 3-folds to surfaces, emphasizing log-Fitting ideals and introducing new methods involving Rank Theorems.

Contribution

It offers a new proof of a key result in algebraic geometry, utilizing log-Fitting ideals and developing innovative techniques related to Rank Theorems.

Findings

Established a new proof of monomialisation from 3-folds to surfaces.

Introduced the concept of log-Fitting ideals in the context of morphism monomialisation.

Developed new methods involving Rank Theorems for algebraic geometry applications.

Abstract

In this paper, we give a new proof of the foundational result, due to S. Cutkosky, on the existence of a monomialisation of a morphism from a 3-fold to a surface. Our proof brings to the fore the notion of log-Fitting ideals, and requires us to develop new methods related to Rank Theorems and log-Fitting ideals.