# Fiches de cours

## Topics in algebraic geometry

#### Enseignant(s) :

Carocci Francesca

English

#### Summary

Algebraic curves and surfaces are the first examples of algebraic varieties to consider. In this course we will study classical topics in the theory of algebraic curves and surfaces applying methods of schemes and cohomology. The course will include many explicit examples and calculations.

#### Content

• Recap: Divisors, Cech cohomology and morphisms to projective space
• Rienann-Roch and Serre duality for curves
• Hurwitz theorem
• Ample line bundles and embeddings
• Regular surfaces
• Intersection theory on regular surfaces
• Monoidal transformations and desingularization

#### Learning Prerequisites

##### Required courses

• Linear algebra,
• Théorie des groupes
• Anneaux et corps
• Rings and Modules
• Modern Algebraic geometry

##### Recommended courses

• Topology I & II
• Algebraic topology
• Differential geometry
• Algebraic number theory

#### Learning Outcomes

By the end of the course, the student must be able to:
• Analyze basic problems in algebraic geometry of curves and surfaces and solve them.

#### Teaching methods

Ex cathedra lecture with exercises

#### Assessment methods

The final grade will be assigned based on the cummulative points of the student obtained from handed in homework solutions and from the written exam. The weights of the two parts are:

30% - homework

70 % - written exam

The homework will be required to hand in any other week.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés

### Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
En construction

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand