Functorial embedded resolution via weighted blowings up

Abstract

We provide a procedure for resolving, in characteristic 0, singularities of a variety $X$ embedded in a smooth variety $Y$ by repeatedly blowing up the worst singularities, in the sense of stack-theoretic weighted blowings up. No history, no exceptional divisors, and no logarithmic structures are necessary to carry this out; the steps are explicit geometric operations requiring no choices; and the resulting algorithm is efficient. A similar result was discovered independently by McQuillan in a manuscript posted on this archive simultaneously.

Introduction rewritten and significantly expanded, proofs streamlined, references updated

References in corpus (1)

• Toroidal orbifolds, destackification, and Kummer blowings up

Cited by in corpus (1)

• Logarithmic resolution via multi-weighted blow-ups