# Logarithmic singularities

- De Rham division lemma (and its generalization)
- Definition of a logarithmic pole: (scalar case). Residues.
- Logarithmic complex: principal lemma on Λ-closedness.
- Principal example: logarithmic complex for the normal crossings. Saito theorem.
- Closed logarithmic 1-forms: complete description. Darbouxian foliations.
- Matrix casse. Conjugacy of the residues along the polar locus. Residues on the normal crossings.
- Schlesinger system: flat connexions with logarithmic poles along the diagonal.
- Flat connexions with first order poles are almost always logarithmic, yet resonances may spoil the pattern.

Recommended reading: the same notes, sect. **3-4**.