Algebraic geometry I - Curves

MATH-328 / 5 crédits

Enseignant: Zanardini Aline

Langue: Anglais

Summary

Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory.

Content

Topics to be covered in this course include:

  • Affine algebraic varieties
  • Plane curves
  • Intersection numbers
  • Projective varieties
  • Bézout's theorem
  • Elliptic curves

 

Learning Prerequisites

Required courses

  • Algebra IV - Rings and modules

 

Recommended courses

Differential geometry II - Smooth manifolds

Learning Outcomes

By the end of the course, the student must be able to:

  • Explain the basic definitions and properties of algebraic varieties, and especially algebraic curves.
  • Express geometric problems in algebraic language and vice versa.
  • Apply basic tools from the algebraic geometry of curves to various problems.
  • Illustrate basic concepts in algebraic geometry with concrete examples.
  • Formulate the main results from the course.

Teaching methods

Ex cathedra course with exercise sessions.

Assessment methods

One final written exam.

Supervision

Office hours No
Assistants Yes
Forum Yes

Resources

Bibliography

The suggested bibliography will be provided during the course.

Notes/Handbook

Handwritten notes will be provided.

Moodle Link

Dans les plans d'études

  • Semestre: Printemps
  • Forme de l'examen: Oral (session d'été)
  • Matière examinée: Algebraic geometry I - Curves
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Type: optionnel

Semaine de référence

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