A smoothness test for higher codimensions. (May 2018)

• Record Type: Journal Article
• Authors: Böhm, Janko; Frühbis-Krüger, Anne
• Is Part Of: Journal of symbolic computation. Volume 86(2018)
• Page Start: 153
• Page End: 165
• Publication Date: 2018-05
• Subjects: Singularities -- Algorithmic smoothness test -- Hironaka resolution of singularities -- Unprojection -- Parallel computation in algebraic geometry; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2017.05.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithm for determining smoothness of algebraic varieties. The algorithm is inherently parallel and does not involve the calculation of codimension-sized minors of the Jacobian matrix of the variety. We also describe a hybrid method which combines the new method with the Jacobian criterion, thus making use of the strengths of both approaches. We have implemented all algorithms in the computer algebra systemSingular . We compare the different approaches with respect to timings and memory usage. The test examples originate from questions in algebraic geometry, where the use of the Jacobian criterion is impractical due to the number and size of the minors involved.