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Functorial embedded resolution via weighted blowings up

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arxiv 1906.07106 v3 pith:RKF3KASV submitted 2019-06-17 math.AG

Dan Abramovich , Michael Temkin , Jaros{l}aw W{l}odarczyk This is my paper
classification math.AG
keywords blowingsembeddedsingularitiesvarietyweightedalgorithmarchiveblowing
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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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Cited by 1 Pith paper

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  1. Universal Characteristic-free Resolution of Singularities, I

    math.AG 2025-07 conditional novelty 7.0 of 10

    An explicit universal blowup process on a birational Grassmannian model is claimed to simultaneously resolve every integral singular Γ-scheme over Q and over finite fields.

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