Effective resolution of singularities

2025/11/10 by Edward Bierstone, Dima Grigoriev, Bierstone, Edward +5
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2511.07639

openalex publication_date 2025/11/10 · openalex created_date 2025/11/13 · openalex updated_date 2026/07/28

Abstract

Consider a projective variety X ⊂ ℙⁿ (over an algebraically closed field of characteristic zero), together with a (reduced) simple normal crossings divisor E ⊂ ℙⁿ, where the degrees of both X and E are at most d. We show there is a pair (n',d') which can be explicitly computed in terms of (n,d), such that (X,E) has a log resolution of singularities (X',E'), where (X',E') can be embedded in ℙ^n' and both X' and E' have degrees at most d' in ℙ^n'.

Citations

• Functoriality in resolution of singularities
• Ideal Membership in Polynomial Rings over the Integers
• Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant

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• Resolution of singularities of pairs preserving semi-simple normal crossings
• Resolution except for minimal singularities I
• Desingularization preserving stable simple normal crossings
• A Simplified Game for Resolution of Singularities
• Blowups and Resolution