A new proof of monomialisation from 3-folds to surfaces

2025/02/25 by Jiang, Yueting
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2502.17996

openalex publication_date 2025/02/25 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28

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.

Related

• Monomialization of Morphisms From 3 Folds to Surfaces
• Monomial resolutions of morphisms of algebraic surfaces
• Trees, parking functions, syzygies, and deformations of monomial ideals
• Semistable reduction in characteristic 0 for families of surfaces and\n three-folds
• Resolution of Singularities for 3-folds in positive characteristic