|
Course by A. V. Vikulova "Algebraic curves"
(February 12–May 7, 2025, Steklov Mathematical Institute, Room 104 (8 Gubkina))
We kindly ask all participants, including remote ones and those
watching recorded videos, to register at this link.
In this course we are going to study algebraic curves, the most ancient
algebraic objects. The tools used in algebraic geometry are very abstract. So we are
going to see how these tools apply in the case of algebraic curves.
Program:
- Algebraic curves. Their description. Definitions: Riemannian surfaces, rational and
regular functions, ring and field of functions.
- Divisors. Linear bundles. Divisors on curves.
- Ramifications. The Riemann-Hurwitz formula.
- Canonical class. The Riemann-Roch theorem.
- Bijection between non-singular algebraic curves and field extensions of
transcendence degree 1.
- Elliptic curves. The elliptic curve group law.
- Automorphisms of algebraic curves. The Hurwitz theorem. The Macbeath
theorem.
- Jacobians of curves.
- The Torelli theorem.
 Lecturer
Vikulova Anastasia Vadimovna
Financial support
The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, agreement no. 075-15-2022-265).
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
|
| Course by A. V. Vikulova "Algebraic curves", February 12–May 7, 2025 |
|
|
May 7, 2025 (Wed) |
 |
| 1. |
Lecture 12. Algebraic curves
A. V. Vikulova
May 7, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
April 30, 2025 (Wed) |
|
| 2. |
Lecture 11. Algebraic curves
A. V. Vikulova
April 30, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
April 23, 2025 (Wed) |
|
| 3. |
Лекция 10. Алгебраические кривые
A. V. Vikulova
April 23, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
April 9, 2025 (Wed) |
|
| 4. |
Lecture 9. Algebraic curves
A. V. Vikulova
April 9, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
April 2, 2025 (Wed) |
|
| 5. |
Lecture 8. Algebraic curves
A. V. Vikulova
April 2, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
March 26, 2025 (Wed) |
|
| 6. |
Lecture 7. Algebraic curves
A. V. Vikulova
March 26, 2025 16:30, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
March 19, 2025 (Wed) |
|
| 7. |
Lecture 6. Algebraic curves
A. V. Vikulova
March 19, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
March 12, 2025 (Wed) |
|
| 8. |
Lecture 5. Algebraic curves
A. V. Vikulova
March 12, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
March 5, 2025 (Wed) |
|
| 9. |
Lecture 4. Algebraic curves
A. V. Vikulova
March 5, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
February 26, 2025 (Wed) |
|
| 10. |
Lecture 3. Algebraic curves
A. V. Vikulova
February 26, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
February 19, 2025 (Wed) |
|
| 11. |
Lecture 2. Algebraic curves
A. V. Vikulova
February 19, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
February 12, 2025 (Wed) |
|
| 12. |
Lecture 1. Algebraic curves
A. V. Vikulova
February 12, 2025 16:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
|
|
|
|
|
|
|
Contact us: