Embedded Curves and Foliations
Hossein Movasati, Paulo Sad
TL;DR
This paper studies the existence and limitations of regular foliations near negatively embedded holomorphic curves, providing conditions for linearization and examples where linearization fails.
Contribution
It establishes the existence of regular foliations with prescribed tangency divisors and presents examples of non-linearizable neighborhoods.
Findings
Existence of regular foliations with prescribed tangency in certain neighborhoods
Examples of neighborhoods that cannot be linearized
Connection to Grauert's linearization theorem
Abstract
We prove the existence of regular foliations with a prescribed tangency divisor in neighborhoods of negatively embedded holomorphic curves; this is related to a linearization theorem due to Grauert. We give also examples of neighborhoods which can not be linearized.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Holomorphic and Operator Theory