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Article Dans Une Revue Mathematische Zeitschrift Année : 2003

Rational curves and rational singularities

Mikhail Zaidenberg

Résumé

We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a $\C^*$-action. For varieties with an isolated singularity, we show that the presence of sufficiently many rational curves outside the singular point strongly affects the character of the singularity. This provides an explanation of classical results due to H.A. Schwartz and G.H. Halphen on polynomial solutions of the generalized Fermat equation.

Dates et versions

hal-00323545 , version 1 (22-09-2008)

Identifiants

Citer

Hubert Flenner, Mikhail Zaidenberg. Rational curves and rational singularities. Mathematische Zeitschrift, 2003, 244 (3), pp.549-575. ⟨10.1007/s00209-003-0497-z⟩. ⟨hal-00323545⟩

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