Credits: 7.5

Type: bridging

Objectives:

To introduce algebraic geometry, starting with the study of affine manifolds of any dimension and the most basic aspects of the theory of smooth curves.

Knowledge:

• Affine algebraic manifolds. Decomposition of irreducible manifolds.
• Morphisms of affine manifolds and the category of affine manifolds.
• Local properties: tangent space, singular points.
• Smooth projective curves.
• Local uniformity. Multiplicity of intersection.
• Bézout's theorem. Plücker's formulas.

Subject-specific competences:

To understand the basic points of the geometry of affine algebraic manifolds and the projective aspects of smooth curves.