Rational curves and rational singularities

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dc.creatorFlenner, Hubert
dc.creatorZaidenberg, Mikhail
dc.date2001-09-28
dc.date.accessioned2026-07-07T04:43:34Z
dc.date.available2026-07-07T04:43:34Z
dc.descriptionWe 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.
dc.description24 pages; uses Paul Taylor's diagrams.tex, see e.g. ftp://ftp.dante.de/tex-archive/macros/generic/diagrams/taylor/V3,88.tex
dc.identifierhttps://arxiv.org/abs/math/0109221
dc.identifierhttp://arxiv.org/abs/math/0109221
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62278
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subjectComplex Variables
dc.subject14J17; 14L30; 13H10
dc.titleRational curves and rational singularities
dc.typetext

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