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Course by A. V. Fonarev "Vector bundles on projective spaces"
(September 10–December 17, 2024, Steklov Mathematical Institute, Room 530 (8 Gubkina))
We kindly ask all participants, including remote ones and those
watching recorded videos, to register at this link.
This is intended to be a "second course" in algebraic geometry. Using vector bundles on projective spaces as the driving set of examples, we will see how various methods of algebraic geometry are applied in practice.
Preliminary program
- Vector bundles and coherent sheaves
- Cohomology of coherent sheaves and basic theorems
- Chern classes
- Grothendieck's theorem, jump lines, Horrocks criterion
- Bundles with different properties: uniform bundles, Tango example, Serre construction
- Topological classification
- Stability in the sense of Mumford and Gieseker
- Splitting of stable bundles
- Beilinson's theorem
- Moduli spaces
 Lecturer
Fonarev Anton Vyacheslavovich
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 |
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| Course by A. V. Fonarev "Vector bundles on projective spaces", September 10–December 17, 2024 |
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December 17, 2024 (Tue) |
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| 1. |
Lecture 14. Vector bundles on projective spaces
A. V. Fonarev
December 17, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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December 10, 2024 (Tue) |
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| 2. |
Lecture 13. Vector bundles on projective spaces
A. V. Fonarev
December 10, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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December 3, 2024 (Tue) |
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| 3. |
Lecture 12. Vector bundles on projective spaces
A. V. Fonarev
December 3, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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November 26, 2024 (Tue) |
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| 4. |
Lecture 11. Vector bundles on projective spaces
A. V. Fonarev
November 26, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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November 19, 2024 (Tue) |
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| 5. |
Lecture 10. Vector bundles on projective spaces
A. V. Fonarev
November 19, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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November 5, 2024 (Tue) |
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| 6. |
Lecture 9. Vector bundles on projective spaces
A. V. Fonarev
November 5, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 29, 2024 (Tue) |
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| 7. |
Lecture 8. Vector bundles on projective spaces
A. V. Fonarev
October 29, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 22, 2024 (Tue) |
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| 8. |
Lecture 7. Vector bundles on projective spaces
A. V. Fonarev
October 22, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 15, 2024 (Tue) |
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| 9. |
Lecture 6. Vector bundles on projective spaces
A. V. Fonarev
October 15, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 8, 2024 (Tue) |
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| 10. |
Lecture 5. Vector bundles on projective spaces
A. V. Fonarev
October 8, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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October 1, 2024 (Tue) |
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| 11. |
Lecture 4. Vector bundles on projective spaces
A. V. Fonarev
October 1, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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September 24, 2024 (Tue) |
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| 12. |
Lecture 3. Vector bundles on projective spaces
A. V. Fonarev
September 24, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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September 17, 2024 (Tue) |
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| 13. |
Lecture 2. Vector bundles on projective spaces
A. V. Fonarev
September 17, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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September 10, 2024 (Tue) |
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| 14. |
Lecture 1. Vector bundles on projective spaces
A. V. Fonarev
September 10, 2024 18:00, Steklov Mathematical Institute, Room 530 (8 Gubkina)
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