First steps on the computation of symmetries of implicit space algebraic curves

Alcázar J. G., Caravantes J., Çoban H. A., Gözütok U., Hermoso C.

Journal of Algebra, vol.701, pp.292-311, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 701
  • Publication Date: 2026
  • Doi Number: 10.1016/j.jalgebra.2026.04.027
  • Journal Name: Journal of Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.292-311
  • Keywords: Computation, Implicit algebraic curves, Symmetry
  • Karadeniz Technical University Affiliated: Yes

Abstract

We present a simple algorithm for computing the Euclidean symmetries of an implicit, smooth space algebraic curve, a problem, up to our knowledge, unsolved so far. The algorithm requires certain hypotheses on the curve and relies on results relating the symmetries of the space curve with the symmetries of an algebraic surface derived from the curve, which can be computed by means of existing algorithms. Thus, our algorithm succeeds unless this surface has infinitely many symmetries, which is a non-generic case.