Approximation by smooth curves near the tangent cone

Details Approximation by smooth curves near the tangent cone Approximation by smooth curves near the tangent cone

1997-11-03

arxiv.org/abs/alg-geom/9711004v2

Journal of Algebra, Volume 266, Issue 1, 2003, pages 154-161

Mathematics

Algebraic Geometry

Extended version of the paper with an application to studying schemes of algebras included

Scientific paper

We show that through a point of an affine variety there always exists a
smooth plane curve inside the ambient affine space, which has the multiplicity
of intersection with the variety at least 3.
This result has an application to the study of affine schemes.

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