Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question

1 Answer 1

up vote 7 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.

share|improve this answer
    
Thanks for your help. –  Strongart Mar 22 '11 at 10:23

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.