“显然”的定义

Aluminiumor

Princeton 流传的数学家们关于“显然”的定义：
If Wedderburn says it's obvious,everybody in the room has seen it ten minutes ago.
If Bohnenblust says it's obvious,it's obvious.
If Bochner says it's obvious,you can figure it out in half an hour.
If von Neumann says it's obvious,you can prove it in three months if you are a genius.
If Lefschetz says it's obvious,it's wrong.

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If Lefschetz says it's obvious,it's wrong.

Lefschetz 大定理：

对复 $n$ 维紧Kähler 流形 $X$, 记其定义中辛形式为 $\omega$,则对自然数 $p,q$, $p + q \leq n$, 有同构\[H^{p,q}(X) \to H^{n-q, n-p}(X),\]由 $x \mapsto x \wedge \omega^{n-p-q}$ 诱导,$H^{p,q}(X)$ 为 Dolbeault 上同调 $H^q(X, \Omega_X^p)$.

证明显然被省略了，看不出来