Conic bundles and iterated root stacks

TL;DR

This paper extends classical results on conic bundles to more general fields by employing advanced geometric techniques like root stacks and destackification.

Contribution

It introduces a novel approach using iterated root stacks and destackification to generalize Sarkisov's results to non-algebraically closed fields.

Findings

Generalization of conic bundle models to perfect fields

Application of root stacks and destackification techniques

Resolution of singularities in the context of conic bundles

Abstract

We generalize a classical result by V. G. Sarkisov about standard models for conic bundles to the case of a not necessarily algebraically closed perfect field, using iterated root stacks, destackification, and resolution of singularities.