We construct infinitely many distinct irreducible smooth structures on $n(S^2\,\times\,S^2)$, the connected sum of n copies of $S^2\,\times\,S^2$, for every odd integer $n\geq 27$.
Given a semistable and nonisotrivial fibered surface f:X→P1, this paper presents the main results on the problem of determining the minimal number of singular fibers that f must admit. The known examples of fibrations with a low number of singular fibers are presented. Some related problems are briefly discussed.
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