On first integrals of holomorphic foliations
Jonny Ardila Ardila
TL;DR
This paper investigates conditions under which holomorphic foliations admit first integrals, focusing on various scenarios including germs of foliations with formal integrals or numerous invariant hypersurfaces.
Contribution
It provides new insights into the existence of first integrals for holomorphic foliations under diverse conditions and scenarios.
Findings
Criteria for the existence of first integrals in different foliation cases
Relationship between invariant hypersurfaces and integrability
Results on formal versus actual first integrals
Abstract
We study the existence of first integral for holomorphic foliations in different scenarios and under different conditions, for instance germ of foliations given by vector fields and having a formal first integral or infinitely many invariant hypersurfaces.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Holomorphic and Operator Theory · Geometry and complex manifolds