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760: 2024/09/27(金)11:02 ID:2zQZH67f(1) AAS
The main result of [Kd-2], whose formulation is attributed to Hodge, is explained as follows.\\

\emph{Generally speaking, our problem to be solved is stated as follows: Establish the existence of the harmonic filed having the given ``characteristic properties'', e.g. the given periods, the given singularities, etc. To solve such problem, we first construct a (not necessarily harmonic) field $\varphi$ having the given characteristic properties, and secondly, using Theorem 5 (Hodge-Kodaira decomposition theorem), decompose $\varphi$ into three parts: $\varphi=e+h+h^*$. The the harmonic part e will give a solution of our problem, under the circumstance that the characteristic properties are not affected by the transformation $\varphi\to e$. Thus our problem is solved by taking the ``orthogonal projection'' e of $\varphi$ on $\mathfrak{E}$.}\\

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