论文标题
谐波形式，霍奇理论和嵌入定理的kodaira
Harmonic Forms, Hodge Theory and the Kodaira Embedding Theorem
论文作者
论文摘要
在这篇说明性文章中，我们概述了谐波差异形式及其后果的理论。 We provide self-contained proofs of the following important results in differential geometry: (1) Hodge theorem, which states that for a compact complex manifold, the de Rham cohomology group is isomorphic to the group of harmonic forms, (2) Hodge decomposition theorem, which states that for a Kähler manifold, the de Rham cohomology group decomposes into the Dolbeault cohomology groups, and (3) Kodaira嵌入定理，该定理给出了何时紧凑的复合歧管的标准，实际上是一种光滑的复杂射击品种。矢量束的基本理论还包含完整性。
In this expository article, we outline the theory of harmonic differential forms and its consequences. We provide self-contained proofs of the following important results in differential geometry: (1) Hodge theorem, which states that for a compact complex manifold, the de Rham cohomology group is isomorphic to the group of harmonic forms, (2) Hodge decomposition theorem, which states that for a Kähler manifold, the de Rham cohomology group decomposes into the Dolbeault cohomology groups, and (3) The Kodaira Embedding theorem, which gives a criterion of when a compact complex manifold is in fact a smooth complex projective variety. The basic theory of vector bundles is also contained for completeness.
