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Показаны различия между двумя версиями страницы.

--- shared:s_k_spherical_2023 [03.05.2025 23:58]
zhilina
+++ shared:s_k_spherical_2023 [09.09.2025 19:24] (текущий)
timashev
@@ Строка 27: / Строка 27: @@
 == Lecture 1 ==
-Two motivating problems: tensor product decomposition of irreducible representations of SL_2 (Clebsch-Gordan formula) and Steiner's conic problem (how many smooth conics are tangent to 5 given conics in general position). Geomertic proof of the Clebsch-Gordan formula using line bundles on **P**^1 × **P**^1 and their restriction to the diagonal. Chasles' solution to Steiner's problem using a peculiar compactification of the space of smooth conics: the //space of complete conics//.
+Two motivating problems: tensor product decomposition of irreducible representations of SL_2 (Clebsch-Gordan formula) and Steiner's conic problem (how many smooth conics are tangent to 5 given conics in general position). Geomertic proof of the Clebsch-Gordan formula using line bundles on **P**<sup>1</sup> × **P**<sup>1</sup> and their restriction to the diagonal. Chasles' solution to Steiner's problem using a peculiar compactification of the space of smooth conics: the //space of complete conics//.
 [[https://www.youtube.com/watch?v=CAMZyKk0uag&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=1&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_1_20.02.2023_102.pdf|notes}}
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@@ Строка 38: / Строка 38: @@
 == Lecture 2 ==
-Digest and references for basic notions and facts from algebraic geometry and theory of algebraic groups: algebraic varieties, Zariski topology, structure sheaf, (quasi)affine and (quasi)projective varieties, morphisms, irreducibility, rational functions, (linear) algebraic groups, their homomorphisms, representations and actions on algebraic varieties, orbits and stabilizers. Geometric quotient, coset spaces and homogeneous varieties, homogeneous fibte bundles, induced representations.
+Digest and references for basic notions and facts from algebraic geometry and theory of algebraic groups: algebraic varieties, Zariski topology, structure sheaf, (quasi)affine and (quasi)projective varieties, morphisms, irreducibility, rational functions, (linear) algebraic groups, their homomorphisms, representations and actions on algebraic varieties, orbits and stabilizers. Geometric quotient, coset spaces and homogeneous varieties, homogeneous fibre bundles, induced representations.
 [[https://www.youtube.com/watch?v=edm55g8BFBw&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=2&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_2_22.02.2023_1324.pdf||notes}}
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@@ Строка 52: / Строка 52: @@
 [[https://www.youtube.com/watch?v=fMgcEwKGpb4&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=3&pp=iAQB|Video]],
-[[https://disk.pku.edu.cn/#/link/C67A6E714DB722B2F3C6C9645D047F25?gns=AC4C6B2B10714F1AB88F4C85417D132B%2F6D40509EC0EB466BAC5DE82646A2BCA8%2F153E3FA28B444BA2B492C582469595C8|notes]]
+{{:specialcourses:spherical:spherical_varieties_lecture_3_27.02.2023_1003.pdf|notes}}
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@@ Строка 63: / Строка 63: @@
 [[https://www.youtube.com/watch?v=iDjGJBoF5PU&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=4&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_4_01.03.2023_1334.pdf|notes}}
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@@ Строка 74: / Строка 74: @@
 [[https://www.youtube.com/watch?v=yW_tJPx8WYQ&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=5&pp=iAQB|Video]],
-[[https://disk.pku.edu.cn/#/link/C67A6E714DB722B2F3C6C9645D047F25?gns=AC4C6B2B10714F1AB88F4C85417D132B%2F6D40509EC0EB466BAC5DE82646A2BCA8%2FC43304DB2CCF45B2B8003E388CCE2313|notes]]
+{{:specialcourses:spherical:spherical_varieties_lecture_5_06.03.2023_954.pdf|notes}}
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@@ Строка 82: / Строка 82: @@
 == Lecture 6 ==
-Symmetric spaces are spherical: end of the proof. //Spherical varieties//: definition and examples (smooth projective quadric hypersurface, space of all quadrics in **P**^n, variety of complete conics, determinantal varieties, toric varieties). Digression: Zariski tangent space, smooth and singular points.
+Symmetric spaces are spherical: end of the proof. //Spherical varieties//: definition and examples (smooth projective quadric hypersurface, space of all quadrics in **P**<sup>n</sup>, variety of complete conics, determinantal varieties, toric varieties). Digression: Zariski tangent space, smooth and singular points.
 [[https://www.youtube.com/watch?v=cCjEHB3nYs8&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=6&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_6_08.03.2023_1333.pdf|notes}}
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@@ Строка 96: / Строка 96: @@
 [[https://www.youtube.com/watch?v=uJAm0SVL7sw&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=7&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_7_13.03.2023_958.pdf|notes}}
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@@ Строка 107: / Строка 107: @@
 [[https://www.youtube.com/watch?v=Ai3cqo0-Ixk&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=8&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_8_15.03.2023_1335.pdf|notes}}
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@@ Строка 118: / Строка 118: @@
 [[https://www.youtube.com/watch?v=SqSMvr-7rzM&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=9&pp=iAQB|Video]],
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+{{ :specialcourses:spherical:spherical_varieties_lecture_9_20.03.2023_956.pdf|notes}}
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@@ Строка 129: / Строка 129: @@
 [[https://www.youtube.com/watch?v=o4K87OYvj4E&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=10&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_10_22.03.2023_1332.pdf|notes}}
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@@ Строка 140: / Строка 140: @@
 [[https://www.youtube.com/watch?v=IA1IIAE-9qc&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=11&pp=iAQB|Video]],
-[[https://disk.pku.edu.cn/#/link/C67A6E714DB722B2F3C6C9645D047F25?gns=AC4C6B2B10714F1AB88F4C85417D132B%2F6D40509EC0EB466BAC5DE82646A2BCA8%2F66B0B6ACF4194087BEF22AC47FD272DE|notes]]
+{{:specialcourses:spherical:spherical_varieties_lecture_11_27.03.2023_953.pdf|notes}}
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@@ Строка 151: / Строка 151: @@
 [[https://www.youtube.com/watch?v=Vbhr5OnxLFo&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=12&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_12_29.03.2023_1331.pdf|notes}}
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@@ Строка 162: / Строка 162: @@
 [[https://www.youtube.com/watch?v=I_9PjNq8wFM&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=13&t=37s&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_13_03.04.2023_1002.pdf|notes}}
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@@ Строка 173: / Строка 173: @@
 [[https://www.youtube.com/watch?v=WsZSe7uWR-c&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=14&pp=iAQB|Video]],
-[[https://disk.pku.edu.cn/#/link/C67A6E714DB722B2F3C6C9645D047F25?gns=AC4C6B2B10714F1AB88F4C85417D132B%2F6D40509EC0EB466BAC5DE82646A2BCA8%2FC24B01DAC1EF4A6FA740C61318F3B03C|notes]]
+{{:specialcourses:spherical:spherical_varieties_lecture_14_05.04.2023_1321.pdf|notes}}
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@@ Строка 184: / Строка 184: @@
 [[https://www.youtube.com/watch?v=RBeob2BJp2g&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=15&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_15_10.04.2023_1000.pdf|notes}}
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@@ Строка 195: / Строка 195: @@
 [[https://www.youtube.com/watch?v=oHzNcLi2G4o&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=16&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_16_12.04.2023_1310.pdf|notes}}
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@@ Строка 206: / Строка 206: @@
 [[https://www.youtube.com/watch?v=JpXYfWNxkm4&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=17&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_17_17.04.2023_1002.pdf|notes}}
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@@ Строка 217: / Строка 217: @@
 [[https://www.youtube.com/watch?v=TBSuA2vHEj8&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=18&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_18_19.04.2023_912.pdf|notes}}
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@@ Строка 228: / Строка 228: @@
 [[https://www.youtube.com/watch?v=QLAEXeW4cus&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=19&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_19_24.04.2023_956.pdf|notes}}
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@@ Строка 239: / Строка 239: @@
 [[https://www.youtube.com/watch?v=ClhJ-Fn0teM&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=20&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_20_26.04.2023_1327.pdf|notes}}
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@@ Строка 250: / Строка 250: @@
 [[https://www.youtube.com/watch?v=iXST04D9-k0&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=21&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_21_08.05.2023_956.pdf|notes}}
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@@ Строка 261: / Строка 261: @@
 [[https://www.youtube.com/watch?v=gb1UeKkjEP4&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=22&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_22_10.05.2023_1327.pdf|notes}}
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@@ Строка 272: / Строка 272: @@
 [[https://www.youtube.com/watch?v=LqjILE7syLw&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=23&pp=iAQB|Video]],
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+{{:specialcourses:spherical:spherical_varieties_lecture_23_15.05.2023_1001.pdf|notes}}
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@@ Строка 283: / Строка 283: @@
 [[https://www.youtube.com/watch?v=WsCBF5oGbAc&list=PLWe9HlG1eGbSEfa39u2YcX5q0NXdAeu79&index=24&pp=iAQB|Video]],
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+{{ :specialcourses:spherical:spherical_varieties_lecture_24_17.05.2023_1337.pdf |notes}}