Sumários

Lecture 6

11 Novembro 2021, 11:00 Davide Masoero

X is a compact Riemann surface of genus g.

We have studied the following:

1. The only holomorphic functions are constant functions
2. Intersection form on the homology and canonical basis
3. Riemann's bilinear relations
4. Newton's polygon


Lecture 5

4 Novembro 2021, 11:00 Davide Masoero

1. Normalisation of (the projectivaisation of) an affine plane curve

2. De Rham Cohomology and singular homology


Lecture 4

28 Outubro 2021, 11:00 Davide Masoero

The lecture was canceled


Lecture 3

21 Outubro 2021, 11:00 Davide Masoero

Topological classification of compact oriented surfaces without boundaries.
The Euler characteristics of a triangulation and the Riemann-Hurwitz formula.
The monodromy representation of a covering map.
The Riemann-Existence theorem.


Lecture 2

14 Outubro 2021, 11:00 Davide Masoero

Review of affine and projective planar curves.
The hyperelliptic curve.
Local models of holomorphic maps between Riemann surfaces. The degree of a proper map.