Smoothtst.lib - a 4-0-3 library for determining smoothness of algebraic varieties: A smoothness test for higher codimensions. 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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References in zbMATH (referenced in 6 articles , 1 standard article )
Showing results 1 to 6 of 6.
- Böhm, Janko; Decker, Wolfram; Frühbis-Krüger, Anne; Pfreundt, Franz-Josef; Rahn, Mirko; Ristau, Lukas: Towards massively parallel computations in algebraic geometry (2021)
- Frühbis-Krüger, Anne; Ristau, Lukas; Schober, Bernd: Embedded desingularization for arithmetic surfaces -- toward a parallel implementation (2021)
- Brown, Gavin; Fatighenti, Enrico: Hodge numbers and deformations of Fano 3-folds (2020)
- Böhm, Janko; Frühbis-Krüger, Anne: A smoothness test for higher codimensions (2018)
- Frühbis-Krüger, Anne: On discriminants, Tjurina modifications and the geometry of determinantal singularities (2018)
- Frühbis-Krüger, Anne; Wewers, Stefan: Desingularization of arithmetic surfaces: algorithmic aspects (2017)