Return to Revisions

Jim's example is good; one can easily construct examples by using elliptic fibrations. Let $$S:=X\times E\rightarrow X$$ be a trivial elliptic fibration with $E$ an elliptic curve. Choose $X$ so that it has a branched cover $X\rightarrow Y$. Then, there will be an elliptic fibration $$S'\rightarrow Y$$ with multiple fibers over the branch points of $X\rightarrow Y$. The difference of the set-theoretic fibers of two branch points with multiplicity $m$ is $m$-torsion in homology.