Algebraic Geometry
| Title | ΑΛΓΕΒΡΙΚΗ ΓΕΩΜΕΤΡΙΑ / Algebraic Geometry |
| Code | 0637 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Spring |
| Coordinator | Dimitrios Poulakis |
| Common | No |
| Status | Active |
| Course ID | 40000025 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 8
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Compulsory Course | 2 | 1 | 10 |
| Academic Year | 2020 – 2021 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600180365
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600180365
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
General Competences
- Adapt to new situations
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Generate new research ideas
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Affine Varieties: Algebraic Sets in Αn, Affine and quasi-affine Varieties, Hilbert's Nullstellensatz, Coordinate Rings, Noether's Spaces. Projective Varieties: Algebraic Sets in Pn, Projective Nullstellensatz, Projective Closure of an Affine Variety. Morphisms of Varieties: Regular Functions, Function Fields of One Variable, Basic properties of Morphisms, Finite Morphisms, Rational maps. Product of Varieties: Product of Affine Varieties, Product of Projective Varieties, Segree's Embedding, Image of a Projective variety. Dimension: Dimension of a Topological Space, Krull's Dimension, Dimension of the Intersection of a Variety with a hypersurface, Dimension and Morphisms. Local Properties.
Keywords
Αffine Varieties - Projective varieties - Algebraic Varieties
Educational Material Types
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | |||||
| Reading Assigment | |||||
| Written assigments | |||||
| Exams | |||||
| Total |
Student Assessment
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Oral Exams (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Δ. Πουλάκης, Αλγεβρική Γεωμετρία, Εκδόσεις Ζήτη, Θεσσαλονίκη 2018.
Additional bibliography for study
1. Dieudonné J. (1974) Cours de Géométrie Algébrique. PUF.
2. Fulton. W. (1978). Algebraic Curves. Benjamin.
3. Harris J. (1992). Algebraic Geometry. Springer Verlag.
4. Kendig K. (1977). Elementary Algebraic Geometry. Springer Verlag.
6. Mumford D. (1995) Algebraic Geometry I. Complex Projective Varieties. Springer Verlag.
7. Perrin D. (1995) Géométrie Algébrique. InterÉditions/Éditions CNRS.
8. Shafarevich I. R. (1994). Basic Algebraic Geometry. Springer Verlag.
9. Smith K. E., Kahanpää, Kekäläinen and Traves W. (2000). An Invitation to Algebraic Geometry. Springer Verlag. 10. Knuz E. (1985). Introduction to Commutative Algebra and Algebraic Geometry. Birkhäuser
Last Update
08-02-2020
