Formal splitting and stack-theoretic normal crossings desingularization

TL;DR

This paper introduces a new stack-theoretic approach to resolving singularities with normal crossings, utilizing a splitting theorem and an existing algorithm for weighted blowings-up to achieve partial desingularization.

Contribution

It provides a simplified, direct method for stack-theoretic resolution of singularities with normal crossings using a splitting theorem and weighted blowings-up.

Findings

Stack-theoretic resolution preserves normal crossings.

A simple, direct method for partial desingularization is developed.

The approach leverages existing algorithms for weighted blowings-up.

Abstract

We show that stack-theoretic resolution of singularities preserving normal crossings (partial desingularization) by weighted blowings-up, can be obtained in a simple direct way from a splitting theorem of the first and third authors, using the algorithm of Abramovich, Temkin and W{\l}odarczyk for resolution of singularities by weighted blowings-up.