The blow-up of a singularity at the module of derivations

2025/10/08 by Paul Barajas, Barajas, Paul, Enrique Chávez-Martínez +3
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2510.07607

Abstract

We study the problem of resolving singularities via the blow-up of the module of derivations. Our main results are a positive answer for the case of curves and log-canonical surface singularities, i.e., a finite sequence of blow-ups along the module of derivations resolves the singularities of such varieties.

Citations

• Nash blowups of normal toric surfaces: the case of one and two segments
• Nash blowup fails to resolve singularities in dimensions four and higher
• The classification of reflexive modules of rank one over rational and minimally elliptic singularities
• On the blow-up of a normal singularity at maximal Cohen-Macaulay modules
• Nash blowups in prime characteristic
• Reflexive modules on normal Gorenstein Stein surfaces, their deformations and moduli
• Nash modification on toric surfaces
• Toric Geometry and the Semple-Nash modification

Related

• Blowups and Resolution
• Resolving plane curves using stack-theoretic blow-ups
• On curves on sandwiched surface singularities
• Resolution of Singularities
• Alterations and resolution of singularities