ALGEBRAIC GEOMETRY
| Title | ΑΛΓΕΒΡΙΚΗ ΓΕΩΜΕΤΡΙΑ / ALGEBRAIC GEOMETRY |
| Code | Θ009 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Chrysostomos Psaroudakis |
| Common | Yes |
| Status | Active |
| Course ID | 600025889 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Spring | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268415
|
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268415
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Learning Outcomes
The students will be able to
1. understand techniques of algebraic geometry with various applications
2. describe varieties
3. describe morphisms between varieties
4. compute the canonical sheaf of rings
5. understand the higher structure of schemes
General Competences
- Work autonomously
- Work in teams
- Generate new research ideas
Course Content (Syllabus)
Algebraic Sets. Varieties. Projective Varieties. The Prime Spectrum. Sheaves. Locally Ringed Spaces. Schemes. Examples of Schemes. Basic Properties and Morphisms of Schemes. Varieties as Schemes. Categories and Schemes. Dimension of Schemes. Tangent Space. Quasi-Coherent Modules.
Keywords
Varieties. Prime Spectrum. Sheaves. Schemes. Categories. Dimension. Tangent Spaces. Quasi-Coherent Modules.
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Seminars | 58 | ||||
| Reading Assigment | 200 | ||||
| Exams | 3 | ||||
| Total | 300 |
Student Assessment
Description
The grading will be obtained in three parts:
(i) Exercise sheets through all semester, percentage of the final degree 20%.
(ii) First written exam in the first half of the course, percentage of the final degree 20%.
(iii) Second written exam in the other half of the course, percentage of the final degree 30%.
The final grade is the overall sum of the above intermediate exams.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative)
- Written Exam with Extended Answer Questions (Formative)
- Written Assignment (Formative)
- Oral Exams (Formative)
- Written Exam with Problem Solving (Formative)
Bibliography
Additional bibliography for study
1) Beltrametti-Carletti-Gallarati-Monti, "Lectures on Curves, Surfaces and Projective Varieties"
2) Shafarevich, "Basic Algebraic Geometry" vol. 1 and 2.
3) Gathmann, "Algebraic Geometry".
4) Liu Qing, "Algebraic Geometry and Arithmetic Curves".
5) Griffiths-Harris, "Principles of Algebraic Geometry".
6) Görtz-Wedhorn, "Algebraic Geometry I, Schemes with Examples and Exercises".
Last Update
01-12-2024
