Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations
Abstract
We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S2. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore, these examples show that fiber sums of holomorphic Lefschetz fibrations do not necessarily admit complex structures.
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