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

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Keywords

Algebraic geometry, algebraic curves, algebraic surfaces

Learning Prerequisites

Required courses

• Linear algebra
• Group Theory
• Rings and Modules
• Modern Algebraic geometry

Recommended courses

• Algebraic topology
• Differential geometry
• Complex Analysis

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

Office hours	Yes
Assistants	Yes
Forum	No

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

• Algebraic Geometry / Hartshorne
• Algebraic Geometry I & II / Görtz-Wedhorn

Références suggérées par la bibliothèque

• The Rising Sea: Foundations of Algebraic Geometry / Vakil

Moodle Link

• https://go.epfl.ch/MATH-535