Square-root Parametrization of Plane Curves

  • Shreeram S. Abhyankar


By calculating the genus of an irreducible algebraic plane curve of degree n in terms of its singularities, we see that, counted properly, the curve can have at most \(\frac{{(n - 1)(n - 2)}} {2}\) double points, and it can be rationally parametrized iff this maximum is reached. If the maximum falls short by one or two, then the curve can still be parametrized by square-roots of rational functions. Such a square-root parametrization is used for factoring certain bivariate polynomials over a finite field.


Galois Group Double Point Plane Curf Hyperelliptic Curve Splitting Field 
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Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Shreeram S. Abhyankar

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