Organized by the DelTaMat project formed Jimmy Santamaria and Charlie Lozano at Universidad Mayor de San Andrés, this two-week course serves as an introduction to algebraic geometry through the study of affine algebraic curves. In the first week, we will explore the category of algebraic sets, laying the foundation for understanding their structure. The second week will focus on plane curves, examining their fundamental properties and key examples.
The course is designed for students interested in developing a geometric intuition for algebraic varieties in a basic level.
Week 1: The Category of affine algebraic sets
Affine algebraic sets (Notes)
Structure of affine algebraic sets (Notes)
Morphisms between affine algebraic sets (Notes)
Topology and Localization of Rings (Notes)
Problems of the first week (Problem Set)
Week 2: Plane Curves and their properties
Plane curves
Multiple points
Local nature of multiplicity
Intersection number
Test