année académique
2024-2025
2025-2026

Titulaire(s) du cours

Špela SPENKO (Coordonnateur)

Crédits ECTS

5

Langue(s) d'enseignement

anglais

Contenu du cours

We start with an introduction to algebraic geometry. We define affine varieties, the Zariski topology, the sheaf of regular functions, morphisms, varieties, projective varieties. This will take about half of the course.

The other half of the course consists of presentations of students on following topics: Grassmannians, birational maps and blowing up, smooth varieties, the 27 lines on a smooth cubic surface, schemes, sheaves of modules, quasi-coherent sheaves, differentials, cohomology of sheaves.

Objectifs (et/ou acquis d'apprentissages spécifiques)

At the end of the course a student should be able to combine algebraic and geometric methods to study geometric objects defined by polynomial equations.

Pré-requis et Co-requis

Connaissances et compétences pré-requises ou co-requises

The student shoud be well acquainted with commutative rings.

Méthodes d'enseignement et activités d'apprentissages

The first part of the course will be given by in person lectures, the second part of the course consists of presentations by students.

Références, bibliographie et lectures recommandées

Andreas Gathmann: Class notes "Algebraic Geometry", https://www.mathematik.uni-kl.de/~gathmann/de/alggeom.php

Miles Reid: Undergraduate Algebraic Geometry, LMS Student Texts, 2013.

Robin Hartshorne: Algebraic Geometry, Graduate Texts in Mathematics, Springer 1977.

Support(s) de cours

  • Université virtuelle

Autres renseignements

Contacts

Špela Špenko, spela.spenko@ulb.be

Campus

Plaine

Evaluation

Méthode(s) d'évaluation

  • Examen écrit
  • Présentation orale

Examen écrit

Présentation orale

Langue(s) d'évaluation

  • anglais
  • (éventuellement français )

Programmes