Holomorphic singular foliations
- Definition of foliation. Different types of equivalence of foliations.
- Equivalence of foliations vs. equivalence of vector fields. Foliations as “phase portraits” of holomorphic vector fields.
- Examples of foliations: Cartesian products, bundles, constant flow on the torus.
- Holonomy of foliations: construction, invariance.
- Singular foliations. Singular locus, its structure. Singular loci of planar foliations. Germs of singular foliations.
Digression: local structure of complex analytic subsets of .
- Complex separatrices and their holonomy.
- Example: holonomy of foliations generated by linear vector fields.
- Suspension: realization of a given holonomy by a foliation.