Indices and residues: from Poincar\'e-Hopf to Baum-Bott, and Marco Brunella
Maur\'icio Corr\^ea, Jos\'e Seade
TL;DR
This paper explores invariants of vector fields and holomorphic foliations, connecting theories of complex analytic singular varieties and singular holomorphic foliations on complex manifolds, highlighting their commonalities.
Contribution
It provides an expository discussion linking invariants across different settings of complex analytic singularities and foliations, emphasizing their interrelations.
Findings
Unifies theories of singular varieties and foliations.
Highlights common invariants and their properties.
Provides insights into the interplay between different complex geometric structures.
Abstract
In this expository article, we study and discuss invariants of vector fields and holomorphic foliations that intertwine the theories of complex analytic singular varieties and singular holomorphic foliations on complex manifolds: two different settings with many points in common.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Geometry and complex manifolds · Holomorphic and Operator Theory