Algebraic geometers study sets that are given by polynomial equations. Many familiar geometric objects can be given in this way, for example the unit circle is just the set of solutions to the equation x^2+y^2=1. In this course we will discuss the basic concepts and methods of algebraic geometry such as affine and projective space, dimension, tangent spaces, intersection theory. Many examples will be treated. This course will be a perfect complement to the courses Introduction to manifolds’ andHomological algebra’. It will be an excellent preparation for master courses dealing with topics in algebraic geometry or Lie groups, such as the national course `Algebraic Geometry’ taught in spring by Prof. dr. B. Edixhoven and Dr. L. Taelman.
Prerequisite
introductory courses on groups, rings and fields, and some topology. That is, the material covered by the local courses Algebra 1-3 and Topologie.
Literature
Robin Hartshorne: Algebraic Geometry. Graduate Texts in Mathematics 52, Springer-Verlag
Methods of instruction
2 hours lecture
Examination
Home work exercises and oral exam