Desingularization of binomial varieties using toric Artin stacks

TL;DR

This paper introduces a method using toric Artin stacks to efficiently desingularize binomial varieties, reducing steps and charts compared to traditional blow-up methods, and extends to multiple hypersurfaces.

Contribution

It presents a novel approach employing fantastacks for desingularization, offering a more efficient alternative to classical blow-up techniques.

Findings

Reduces the number of steps in desingularization process

Decreases the complexity and number of charts involved

Extends to partial simultaneous normal crossings desingularization

Abstract

We show how the notion of fantastacks can be used to effectively desingularize binomial varieties defined over algebraically closed fields. In contrast to a desingularization via blow-ups in smooth centers, we drastically reduce the number of steps and the number of charts appearing along the process. Furthermore, we discuss how our considerations extend to a partial simultaneous normal crossings desingularization of finitely many binomial hypersurfaces.