Algebraic Curves
| Title | ΑΛΓΕΒΡΙΚΕΣ ΚΑΜΠΥΛΕΣ / Algebraic Curves |
| Code | 0135 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | No |
| Status | Active |
| Course ID | 40000304 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 13
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2022 – 2023 |
| Class Period | Spring |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Class ID | 600226549
|
Course Type 2021
Specific Foundation
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/1/600226549
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Learning Outcomes
Students will know the basic concepts of algebraic geometry, projective space and curves in the projective plane. They will view nonsingular algebraic curves as examples of Riemann surfaces.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Make decisions
- Work autonomously
- Work in an international context
- Work in an interdisciplinary team
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
An introduvtion to algebraic geometry concentrating on algebraic curves. We will study affine and projective algebraic varieties- in particular Plane algebraic curves and Projective algebraic curves -Hilbert's Nullstellensatz, Intersection number - Bezout's theorem - Multiplicity and intersection number, divisors.
Educational Material Types
- Notes
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Student Assessment
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Reading Assigment | 120 | 4 | |||
| Exams | |||||
| Total | 159 | 5.3 |
Student Assessment
Description
Homework and presentations: 20%
Mideterm: 40%
Final Exam: 40%
Bibliography
Course Bibliography (Eudoxus)
Ι. Αντωνιάδης, Α. Κοντογεώργης: Αλγεβρικές Καμπύλες, μια εισαγωγή στην Αλγεβρική Γεωμετρία, Καλλιπος 2021
Δ. Πουλάκης, Εισαγωγή στη Γεωμετρία των Αλγεβρικών Καμπυλών, Εκδόσεις Ζήτη, Θεσσαλονίκη 2006.
Additional bibliography for study
A. Gathmann: Plane Algebraic Cuves, Class Notes TU Kaiserlautern 2018
W. Fulton, Algebraic Curves-An introduction to Algebraic Geometry, 2008
Last Update
05-02-2023
