Singular algebraic curves over finite fields

  • Despina Polemi
  • Takis Sakkalis
Coding and Cryptography
Part of the Lecture Notes in Computer Science book series (LNCS, volume 793)


This paper presents algorithms for the identification and resolution of rational and non-rational singularities (by means of blowings-up) of a projective plane curve C: F(x1, x2, x3)=0 with coefficients in a finite field k. As a result, the genus of the curve is computed. In addition the running time of the algorithms are also analyzed.

Key words and phrases

finite field rational points non-rational points singular points blowing-up process genus 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Despina Polemi
    • 1
  • Takis Sakkalis
    • 2
  1. 1.Department of MathematicsState University of New YorkFarmingdale
  2. 2.Department of Mathematical SciencesOakland UniversityRochester

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