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- Title
Logarithmic resolution via weighted toroidal blow-ups.
- Authors
Quek, Ming Hao
- Abstract
Let X be a fs logarithmic scheme which admits a strict closed embedding into a logarithmically smooth scheme Y over a field k of characteristic zero. We construct a simple and fast procedure to make a functorial logarithmic resolution of X, where the end result is, in particular, a stack-theoretic modification X' → X such that X' is logarithmically smooth over k. In particular, if X is a finite-type k-scheme embedded in a smooth k-scheme Y, the procedure not only shares the same desirable features as the “dream resolution algorithm” of Abramovich–Temkin–W lodarczyk [Functorial embedded resolution via weighted blowings up, arxiv: 19'6.'71'6] but also accounts for a key feature of Hironaka’s Main Theorem I in [Resolution of singularities of an algebraic variety over a field of characteristic zero. I, Ann. of Math. 79 (1964), no. 1, 1'9–2'3] which was not addressed in the Abramovich–Temkin–W lodarczyk paper. As a consequence, we recover a different and simpler approach to Hironaka’s resolution of singularities in characteristic zero.
- Subjects
LOGARITHMIC integrals; MATHEMATICAL singularities; ZERO (The number); ALGEBRAIC stacks; ALGORITHMS
- Publication
Algebraic Geometry, 2022, Vol 9, Issue 3, p311
- ISSN
2313-1691
- Publication type
Article
- DOI
10.14231/AG-2022-010