Displaying similar documents to “Cubic differential forms and the group law on the Jacobian of a real algebraic curve”

Curves on a ruled cubic surface.

John Brevik, Francesco Mordasini (2003)

Collectanea Mathematica

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For the general ruled cubic surface S (with a double line) in P3 = P3 sub k, k any algebraically closed field, we find necessary conditions for which curves on S can be the specialization of a flat family of curves on smooth cubics. In particular, no smooth curve of degree > 10 on S is such a specialization.

Affine plane curves with one place at infinity

Masakazu Suzuki (1999)

Annales de l'institut Fourier

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In this paper we give a new algebro-geometric proof to the semi-group theorem due to Abhyankar-Moh for the affine plane curves with one place at infinity and its inverse theorem due to Sathaye-Stenerson. The relations between various invariants of these curves are also explained geometrically. Our new proof gives an algorithm to classify the affine plane curves with one place at infinity with given genus by computer.