vix.ing · top · new · best · stats · spec

Computational aspects of the higher Nash blowup

2014/11/11 by Daniel Duarte, Duarte, Daniel
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.1411.2676

21 pages

arxiv created 2014/11/11 · openalex publication_date 2014/11/11 · arxiv updated 2014/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The higher Nash blowup of an algebraic variety replaces singular points with limits of certain spaces carrying higher-order data associated to the variety at non-singular points. In this note we will define a higher-order Jacobian matrix that will allow us to make explicit computations concerning the higher Nash blowup of hypersurfaces. Firstly, we will generalize a known method to compute the fiber of this modification. Secondly, we will give an explicit description of the ideal whose blowup gives the higher Nash blowup. As a consequence, we will deduce a higher-order version of Nobile's theorem for normal hypersurfaces.

Related