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arXiv · 1906.07106

Functorial embedded resolution via weighted blowings up

Dan Abramovich·Michael Temkin·Jarosław Włodarczyk
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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.

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Dan Abramovich, Michael Temkin, Jarosław Włodarczyk. 2019-06-17. Functorial embedded resolution via weighted blowings up. https://doi.org/10.2140/ant.2024.18.1557

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