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, cilt.701, ss.292-311, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 701
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.jalgebra.2026.04.027
  • Dergi Adı: Journal of Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.292-311
  • Anahtar Kelimeler: Computation, Implicit algebraic curves, Symmetry
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.