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As we know,the flabby sheaf and the fine sheaf are all acyclic,but does one imply another?I need some examples to distinguish them,who can help me?

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up vote 8 down vote accepted

Sheaf of $C^{\infty}$ functions on paracompact manifold $X$ is fine because exists partitions of unity on $X$. But is not flabby because you cannot extend function on open subset $U$ if function blow up at frontier of $U$.
Constant sheaf with values in $\mathbb Z$ is flabby on irreducible algebraic variety but not fine.

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Thanks for your help. – Strongart Mar 22 '11 at 10:23

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