A smoothness test for higher codimensions

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Janko Böhm
  • Anne Frühbis-Krüger

Organisationseinheiten

Externe Organisationen

  • Technische Universität Kaiserslautern
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)153-165
Seitenumfang13
FachzeitschriftJournal of Symbolic Computation
Jahrgang86
Frühes Online-Datum5 Mai 2017
PublikationsstatusVeröffentlicht - Mai 2018

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 system SINGULAR. 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.

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A smoothness test for higher codimensions. / Böhm, Janko; Frühbis-Krüger, Anne.
in: Journal of Symbolic Computation, Jahrgang 86, 05.2018, S. 153-165.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Böhm J, Frühbis-Krüger A. A smoothness test for higher codimensions. Journal of Symbolic Computation. 2018 Mai;86:153-165. Epub 2017 Mai 5. doi: 10.1016/j.jsc.2017.05.001
Böhm, Janko ; Frühbis-Krüger, Anne. / A smoothness test for higher codimensions. in: Journal of Symbolic Computation. 2018 ; Jahrgang 86. S. 153-165.
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