Sergei Yakovenko's blog: on Math and Teaching

Thursday, May 29, 2008

Lecture 12 (May 29, 2008)

Logarithmic singularities

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

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

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