**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.

Preliminary reading before the meeting: Textbook section 2 (printing disabled) andFirst Aid (sections A6-A8).

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A request: Sergei, could you post the book’s updated reference list, since there were few changes from the published draft?

Comment by Roy Malka — Saturday, November 10, 2007 @ 10:45 |

Roy: here it goes: Bibliography.

Comment by Sergei Yakovenko — Sunday, November 11, 2007 @ 9:36 |

It is too bad there was no time for the digression on local structure of analytic sets…

Comment by Gal Binyamini — Monday, November 12, 2007 @ 11:29 |

Gal: I am afraid that I would be able only to formulate the results in any case. Look for the first aid.

Comment by Sergei Yakovenko — Tuesday, November 13, 2007 @ 6:17 |