Rational curves and rational singularities
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
Complex Variables
Abstract
We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a -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.
Cite
@article{arxiv.math/0109221,
title = {Rational curves and rational singularities},
author = {Hubert Flenner and Mikhail Zaidenberg},
journal= {arXiv preprint arXiv:math/0109221},
year = {2007}
}
Comments
24 pages; uses Paul Taylor's diagrams.tex, see e.g. ftp://ftp.dante.de/tex-archive/macros/generic/diagrams/taylor/V3,88.tex