The aim of the course is to introduce the main concepts, tools, and techniques related to algebraic geometry. The learning objectives of the course are for students to understand the basic structures and properties and to develop the knowledge needed to tackle practical problems.
Course Prerequisites
The basic courses in geometry and algebra and a course in commutative algebra
Teaching Methods
Lectures, exercise sessions.Seminari.
Assessment Methods
There will be an oral exam. It will consist of two parts: One part involves the development of an exercise and concrete examples, and the other involves theoretical questions.
Texts
Igor R. Shafarevich - Basic Algebraic Geometry vol 1/2 Hartshorne, Robin. Algebraic geometry. (Graduate texts in mathematics: 52). B. Griffiths; Harris - "Principles of Algebraic Geometry". J. Harris Algebraic Geometry: A First Course
Contents
Affine and projective varieties defined over an algebraically closed field. Regular maps and rational maps. Separate morphisms and proper maps. Concrete examples: Grassmannians, hypersurfaces Segre embeddings and products. Dimension theory and applications. Tangent space and Bertini's theorem. An overview of coherent sheaves and the theory of schemes.
