Sumários

Not Taught.

11 Março 2020, 10:30 Davide Masoero

Due to the Covid19 outbreak the class was canceled


Algebraic curves, and their normalisation

4 Março 2020, 10:30 Davide Masoero

The projective space CP²
Compactification of an affine plane curve in CP^2
Normalisation of an affine plane curve
The normalisation of the hyper-elliptic curves

References: Donaldon 3.2 and 4.2.3


Proper mappings and Riemann Existence Theorem

26 Fevereiro 2020, 10:30 Davide Masoero

Section 4.1 of Donaldson book: local behaviour of map between Riemann surfaces, degree, proper maps, monodromy representation, Riemann existence theorem, Riemann-Hurwitz formula


Basic theory

19 Fevereiro 2020, 10:30 Davide Masoero

Implicit function theorem in the holomorphic category
Sqrt(P(z)), with P a polynomial, as a single valued function in the cut plane
Definition of Riemann surfaces, first examples
Classification of orientable surfaces
The Riemann surface of an affine smooth planar curve