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商品描述
This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.
商品描述(中文翻譯)
這是一本關於凱勒幾何（Kaehlerian geometry）和霍奇結構（Hodge structure）的現代入門書籍。內容從變數、複流形（complex manifolds）、全純向量束（holomorphic vector bundles）、層（sheaves）和上同調理論（cohomology theory）開始（後者的處理方式比幾何學中通常的更具理論性）。本書的高潮是霍奇分解定理（Hodge decomposition theorem）。在此之間，作者證明了凱勒恆等式（Kaehler identities），這導致了困難的萊夫謝茨定理（hard Lefschetz theorem）和霍奇指數定理（Hodge index theorem）。本書的第二部分探討了這些結果在多個方向上的意義。
