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Rational curves and rational singularities

Rational curves and rational singularities  We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a ℂ*-action. For varieties with an isolated singularity, covered by a family of rational curves with a general member not passing through the singular point, we show that this singularity is rational. In particular, this provides an explanation of classical results due to H. A. Schwartz and G. H. Halphen on polynomial solutions of the generalized Fermat equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Rational curves and rational singularities

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References (68)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag Berlin Heidelberg
Subject
Legacy
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-003-0497-z
Publisher site
See Article on Publisher Site

Abstract

 We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a ℂ*-action. For varieties with an isolated singularity, covered by a family of rational curves with a general member not passing through the singular point, we show that this singularity is rational. In particular, this provides an explanation of classical results due to H. A. Schwartz and G. H. Halphen on polynomial solutions of the generalized Fermat equation.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Jul 1, 2003

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