Abstract
We review results about the geography problem of complex, symplectic and Einstein 4-manifolds. Finally we discuss the same problem for Lefschetz fibrations. We show that in the geography of symplectic 4-manifolds and Lefschetz fibrations the slopes α = c1 2/c2 do not admit gaps — following similar results of Sommese in the complex case.
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Stipsicz, A.I. The Geography Problem of 4-Manifolds with Various Structures. Acta Mathematica Hungarica 87, 267–278 (2000). https://doi.org/10.1023/A:1006719917276
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DOI: https://doi.org/10.1023/A:1006719917276