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Seminar by D. O. Orlov, Yu. G. Prokhorov and C. A. Shramov "Rationality problem in algebraic geometry"
(September 17, 2025–April 29, 2026, 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.
The goal of the seminar is to study the theory of intermediate Jacobians and apply it to prove non-rationality of some Fano threefolds and conic bundles.
In particular, we are going to discuss the degeneration method for intermediate Jacobians, and use it to show that cubic threefolds and quartic double solids
are non-rational. Also, we will consider intermediate Jacobians of Fano threefolds with large symmetry groups, and discuss a generalization of the theory
of intermediate Jacobians for varieties over algebraically non-closed fields.
 Seminar organizers
Orlov Dmitri Olegovich
Prokhorov Yuri Gennadievich
Shramov Constantin Aleksandrovich
Financial support
The seminar is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, agreement no. 075-15-2025-303).
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center |
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| Seminar by D. O. Orlov, Yu. G. Prokhorov and C. A. Shramov "Rationality problem in algebraic geometry", September 17, 2025–April 29, 2026 |
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April 29, 2026 (Wed) |
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| 1. |
Seminar 21. Insufficiency of intermediate Jacobian as an obstruction to rationality
N. Andrusov
April 29, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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April 22, 2026 (Wed) |
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| 2. |
Seminar 20. Sarkisov criterion for non-rationality of conic bundles
B. Zhdanov
April 22, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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April 15, 2026 (Wed) |
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Seminar 19. Extension of conic bundles
K. S. Zyubin
April 15, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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April 1, 2026 (Wed) |
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Seminar 18. Non-rationality of a quartic threefold
Ks. Kvitko
April 1, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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March 25, 2026 (Wed) |
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Seminar 17. Birational rigidity
A. K. Sonina
March 25, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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March 11, 2026 (Wed) |
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Seminar 16. Intermediate Jacobians over algebraically non-closed fields
A. V. Krüger
March 11, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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March 4, 2026 (Wed) |
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Seminar 15. Intermediate Jacobians of symmetric threefolds
N. Savelko
March 4, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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February 25, 2026 (Wed) |
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Seminar 14. Non-rationality of a general cubic threefold via a degeneration to the Segre cubic (part 2)
M. A. Ovcharenko
February 25, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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February 18, 2026 (Wed) |
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Seminar 13. Non-rationality of a general cubic threefold via a degeneration to the Segre cubic
M. A. Ovcharenko
February 18, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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February 11, 2026 (Wed) |
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Seminar 12. Degeneration method for intermediate Jacobians
I. Shatova
February 11, 2026 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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December 3, 2025 (Wed) |
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| 11. |
Seminar 11. Intersection of three quadrics
M. Glukhov
December 3, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 26, 2025 (Wed) |
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Seminar 10. Conic bundles with discriminant curve of genus 6
M. A. Ovcharenko
November 26, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 19, 2025 (Wed) |
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Seminar 9. Intermediate Jacobian of a conic bundle
I. Zhurin
November 19, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 12, 2025 (Wed) |
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| 14. |
Seminar 8. Intermediate Jacobian
K. S. Zyubin
November 12, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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November 5, 2025 (Wed) |
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| 15. |
Seminar 7. Distinguishing Prym varieties from Jacobians
Ks. Kvitko
November 5, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 29, 2025 (Wed) |
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| 16. |
Seminar 6. Donagi tetragonal construction
V. Mamonov
October 29, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 22, 2025 (Wed) |
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| 17. |
Seminar 5. Prym varieties of double covers of hyperelliptic and trigonal curves
N. Andrusov, A. Andronova
October 22, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 15, 2025 (Wed) |
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| 18. |
Seminar 4. Prym variety
O. Mukhametov
October 15, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 8, 2025 (Wed) |
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Seminar 3. Jacobian of a curve
A. Zlobin
October 8, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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October 1, 2025 (Wed) |
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Seminar 2. Abelian varieties
A. K. Sonina
October 1, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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September 17, 2025 (Wed) |
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| 21. |
Seminar 1. A survey of the theory of intermediate Jacobians
C. A. Shramov
September 17, 2025 18:00, Steklov Mathematical Institute, Room 104 (8 Gubkina)
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