Course Overview

This course is an introduction to Algebraic Geometry.

Learning Achievement

Competence

Course prerequisites

> Applicants should:

- Have completed, with good results, a Bachelor of science degree in
Mathematics or equivalent with aspecial focus on Algebra, Geometry and
Number Theory.
- Have thorough proficiency in written and spoken English.

Grading Philosophy

Exams take place in December

Course schedule

> Program:

- Preliminary on commutative algebra (tensor product, localization,
Hilbert theorem).
- Sheaves and their cohomologies.
- Affine schemes, schemes, morphisms of schemes.
- Projective schemes.
- Topological properties (irreducible components,connected
components, dimension).
- Algebraic properties (reduced schemes, integralschemes, noetherian
schemes).
- Some classes of morphisms (morphisms of finite type,proper
morphisms, projective morphisms).
- Fiber products and base change.
- Algebraic curves (equivalence with the function fields of one
variable; divisors).

> Bibliography:

- Q. Liu: Algebraic Geometry and Arithmetic curves,Oxford GTM 6,
Oxford Univ. Press, 2006.
- R. Hartshorne: Algebraic geometry, Graduate Texts inMath., 52,
Springer-Verlag, 1977.

Course type

> Lectur and practical work: - 57 course hours, - 200 hours of personal study.

Online Course Requirement

Instructor

Other information

- This course is part of the ALGANT Joint Master Program.

- For further information on the program structure, partner
institutions, scholarship opportunities, etc., please visit: ALGANT
Erasmus Mundus. [http://algant.eu/]

Duration: 12 weeks (Fall Semester)

Language of instruction: English
Mode of delivery: Face-to-face teaching

Site for Inquiry