Algebraic geometry III - selected topics

Summary

This course is an introduction to the theory of algebraic curves and surfaces. An important aim of the course is to develop geometric intuition while using the language of schemes developed in the basic algebraic geometry course, thus building a solid foundation for further study.

Content

Keywords

Algebraic geometry, algebraic curves, algebraic surfaces

Learning Prerequisites

Required courses

• Algebra IV - Rings and modules
• Algebraic geometry I - Curves
• Algebraic geometry II - schemes and sheaves

Recommended courses

• Differential geometry II - smooth manifolds
• Complex manifolds

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
• Use the statements of basic theorems like Riemann-Roch, Serre duality, etc, and understand their proofs.
• Reason intuitively about the geometry and topology of curves over the complex and finite fields.
• Compute geometric and birational invariants of curves and surfaces in basic examples.

Teaching methods

2h lectures+2h exercise sessions weekly.

Assessment methods

Oral Exam

Supervision

Resources

Bibliography

We will follow mainly:

• Hartshorne, Algebraic Geometry
• Vakil, The Rising Sea: Foundations of Algebraic Geometry
• Görtz-Wedhorn, Algebraic Geometry I & II

Ressources en bibliothèque

• Find the references at the Library

Moodle Link

• https://go.epfl.ch/MATH-535