Rational curves and rational singularities

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
24 pages; uses Paul Taylor's diagrams.tex, see e.g. ftp://ftp.dante.de/tex-archive/macros/generic/diagrams/taylor/V3,88.tex

Keywords

Algebraic Geometry, Commutative Algebra, Complex Variables, 14J17; 14L30; 13H10

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/62278

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0109221
 http://arxiv.org/abs/math/0109221

Collections

arXiv