Instituto Nacional de Matemática Pura e Aplicada
Complex variables
Sala 344, Mondays, Fridays, 13:30-14:00, March-June 2019
Annotation
Course materials
- Part 1: Differential forms and Cauchy theorem
- Part 2: Complex manifolds, almost complex manifolds and sheaves.
- Part 3: Weierstrass preparation theorem.
- Part 4: Weierstrass division theorem.
- Part 5: Ring of germs: algebraic properties
- Part 6-7: Galois theory.
- Part 8: Hilbert's Nullstellensatz.
- Part 9-12: Meromorphic functions, divisors, dimension, finite morphisms.
- Reading assignment: Robert C. Gunning, Hugo Rossi, Analytic functions of several complex variables, Sections IIIA, IIIB.
- Normalization and finite dependence:
- M. F. Atiyah, I. G. MacDonald,
"Introduction to Commutative Algebra" ,
Chapter 5.
- B. L. van der Waerden, J. R. Schulenberger, Algebra, Volume II,
Chapter 17.
- J.-P. Demailly, Complex analytic and differential geometry,
Chapter II, section 7.
- Handout 9:
Rückert's Nullstellensatz.
- Handout 10:
Smooth points and meromorphic maps.
- Handout 11:
Divisors, dimension, maximum principle.
- Handout 12:
Finite morphisms.
Other materials