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1 vote

Is the "addition" of flat morphisms flat?

This shouldn't be the case. Let $X = Y = \mathbb{P}^1$ with projective coordinates $[x:y]$, $f = id_X$. $F = \mathcal{O}_X$, $G = \mathcal{O}_X \oplus \mathcal{O}_X(1)$. Let $\phi_1 = id \oplus x$ an …
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