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Create: 2025-06-24 Update: 2025-07-06 04:03:12

https://mccme.ru/free-books/dubna/vva-volumes.pdf

стала бесплатно доступна электронная версия книги «Ветвящиеся объёмы и группы отражений» В.А.Васильева по его рассказам на ЛШСМ

«Рассматривается восходящая к Архимеду и Ньютону задача о зависимости объема, отсекаемого плоскостью от ограниченного тела, от этой плоскости. В частности, мы докажем гипотезу В.И.Арнольда о том, что для тела с гладкой границей в четномерном пространстве этот объем не может алгебраически зависеть от коэффициентов уравнения плоскости, и приведем геометрические препятствия к такой алгебраичности в нечетномерном случае.

В книге рассказано об истории вопроса и о методах, позволяющих решать такие и подобные задачи (включая задачи о разрешимости уравнений в радикалах): теории монодромии, аналитическом продолжении, группах преобразований, порожденных отражениями, и топологии комплексных многообразий.»

можно также купить бумажную книгу:
https://biblio.mccme.ru/node/74704

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vva-volumes.pdf

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