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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 [16.07.2025 14:35] (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 41: / Строка 41: @@
 [[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]],
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+{{: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]],
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+{{: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]],
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+{{: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]],
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+{{: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}}