Arc lifting for the Nash manifold
John Atwell Moody
TL;DR
This paper proves a theorem providing conditions to lift holomorphic arcs to the Nash manifold's smooth locus and introduces a valuation theorem, advancing the understanding of Nash manifolds in algebraic geometry.
Contribution
It establishes necessary and sufficient conditions for arc lifting and presents a new valuation theorem related to Nash manifolds.
Findings
Conditions for lifting holomorphic arcs are characterized.
A new valuation theorem for Nash manifolds is proven.
The results deepen the understanding of the structure of Nash manifolds.
Abstract
A theorem of Functorial Affinization of Nash's manifold is proven here giving necessary and sufficient conditions to lift a holomorphic arc to the smooth locus of the Nash manifold. In addition a theorem about valuations is proven.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Algebra and Geometry · Geometry and complex manifolds