Nash modification on toric curves

2018/08/16 by Daniel Duarte, Duarte, Daniel, Daniel Green Tripp +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1808.05688

15 pages

arxiv created 2018/08/16 · openalex publication_date 2018/08/16 · arxiv updated 2018/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the problem of resolution of singularities of toric curves by iterating Nash modification. We give a bound on the number of iterations required to obtain the resolution. We also introduce a different approach on counting iterations by dividing the combinatorial algorithm of Nash modification of toric curves into several division algorithms.

Cited by

• Classification of normal toric surfaces resolved by a single Nash blowup
• Non-normalized Nash blowup fails to resolve singularities in dimension three

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