Contents and course program

This course is an introduction to Algebraic Geometry.
The objects studied in Algebraic Geometry are algebraic varieties, which are loosely speaking geometric objects locally defined by common zeroes of polynomials. The study of the geometric properites of algebraic varieties is mainly carried out by means of Commutative Algebra.
In this course we will introduce, at a basic level, some of the main concepts and tools of Algebraic Geometry, such as:
- affine and projective varieties;
- Algebraic tangent spaces, singularities and blow ups;
- maps between varieties and fields of fractions;
- maps in projective spaces and linear systems;
A great focus will be given to concrete classical constructions and computations, mainly in the case of complex projective curves and surfaces.
The course will be as much as possible self-contained: the results in Commutative Algebra needed will be recalled during the course.

Teaching methods

Lessons and home exercises to be discussed together.