2024
Introduction to Algebraic Geometry
Name: Introduction to Algebraic Geometry
Code: MAT14353M
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Presentation
In this CU affine and projective algebraic varieties are studied, as well as the main objects of study of classical algebraic geometry.
Sustainable Development Goals
Learning Goals
- Knowledge: having contact with algebraic sets and algebraic varieties, mainly algebraic curves, the central objects in algebraic geometry, and experiencing problems in this context, applying general algebraic techniques and creating strategies that are specific to each problem; exploring applications of algebraic geometry in other fields of mathmatics.
- Skills and Competences: developing abstract reasoning and the capacity of finding strategies to solve new problems.
- Skills and Competences: developing abstract reasoning and the capacity of finding strategies to solve new problems.
Contents
Affine algebraic sets.
Hilbert basis theorem.
Hilbert's Nullstellensatz.
Affine varieties.
Local properties of plane curves.
Projective varieties and projective plane curves.
Hilbert basis theorem.
Hilbert's Nullstellensatz.
Affine varieties.
Local properties of plane curves.
Projective varieties and projective plane curves.
Teaching Methods
Problem-solving sessions, where students are invited to work on their own or in small groups, with some moments of exposition or discussion involving the whole class.
The evaluation may be either continuous, done through two or three oral presentations, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final classification.
The evaluation may be either continuous, done through two or three oral presentations, done preferably during the classes, weighting 100% of the classification, the number of which is to be defined by the professor who is responsible for the course unit in each academic year, or by a final exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process; the elements of formative evaluation will have no weight on the final classification.
