Let $F$, $G$ be two locally free sheaf on $X$, and let $\phi:F\rightarrow G$ is injective. Then why is that $\phi$ may not be injective on all fibers? Are we still regarding this map as morphism of sheafs, so injective should be equivalent to injective on all fibres?
2026-03-26 14:25:19.1774535119
Injectivity of locally free sheaf
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