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 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.