[過去ﾛｸﾞ] 「名誉教授」のスレ (1002ﾚｽ)

「名誉教授」のスレ http://rio2016.5ch.net/test/read.cgi/math/1693560419/

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760: １３２人目の素数さん [] 2024/09/27(金) 11:02:50.17 ID:2zQZH67f 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 $\mathfrak{E}$.}\\ http://rio2016.5ch.net/test/read.cgi/math/1693560419/760

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