# Coursebooks

## Introduction to Algebraic geometry

Patakfalvi Zsolt

English

#### Summary

Algebraic geometry is a central subject of modern mathematics, lying between differential geometry and number theory. The course will give an introduction to algebraic geometry, arriving at the end to the Riemann-Roch theorem for curves and to Bézout's theorem.

#### Content

• Quasi-projective varieties
• Dimension
• Regular and rational functions
• Birational equivalence
• Regular varieties
• Normal varieties
• Divisors
• Linear systems
• Sheaves
• Cech cohomology
• Riemann-Roch theorem for curves

#### Learning Prerequisites

##### Required courses

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

##### 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 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 on a weekly basis.

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.

#### Supervision

 Office hours No Assistants Yes Forum No

#### Resources

##### Notes/Handbook

There will be typed (latex) notes distributed on moodle.

### In the programs

• Mathematics - master program, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Introduction to Algebraic geometry
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 2
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Introduction to Algebraic geometry
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 4
• Semester
Spring
• Exam form
Written
• Credits
5
• Subject examined
Introduction to Algebraic geometry
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

### Reference week

MoTuWeThFr
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
Under construction
Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German