Displaying similar documents to “On the logarithmic plurigenera of algebraic surfaces”

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.

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.

Explicit resolutions of double point singularities of surfaces.

Alberto Calabri, Rita Ferraro (2002)

Collectanea Mathematica

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Locally analytically, any isolated double point occurs as a double cover of a smooth surface. It can be desingularized explicitly via the canonical resolution, as it is very well-known. In this paper we explicitly compute the fundamental cycle of both the canonical and minimal resolution of a double point singularity and we classify those for which the fundamental cycle differs from the fiber cycle. Moreover we compute the conditions that a double point singularity imposes to pluricanonical...