SUBJECT
Title
Supplementary chapters of topology I. – Topology of singularities. (special material)
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
A short description of the course:
- Complex algebraic curves
- holomorphic functions of many variables
- implicit function theorem
- smooth and singular analytic varieties
- local singularities of plane curves
- Newton diagram, Puiseux theorem
- Resolution of plane curve singularities
- Resolution graphs
- topology of singularities, algebraic knots
- Milnor fibration
- Alexander polynomial, monodromy, Seifert matrix
- Projective plane curves
- Dual curve, Plucker formulae
- Genus, Hurwitz-, Clebsh, Noether formulae
- Holomorphic differential forms
- Abel theorem
Readings
- C. T. C. Wall: singular points of plane curves, London Math. Soc. Student Texts 63.
- F. Kirwan: Complex Algebraic Curves, London Math. Soc. Student Texts 23.
- E. Brieskorn, H. Korner: Plane Algebraic Curves, Birkhauser