Functorial embedded resolution via weighted blowings up

Dan Abramovich, Michael Temkin, Jarosław Włodarczyk

Research output: Contribution to journalArticlepeer-review

Abstract

We provide a simple 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 (2020).

Original languageEnglish
Pages (from-to)1557-1587
Number of pages31
JournalAlgebra and Number Theory
Volume18
Issue number8
DOIs
StatePublished - 2024

Keywords

  • algebraic stacks
  • resolution of singularities
  • weighted blowings up

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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