On the holomorphicity of genus two Lefschetz fibrations
Abstract
We prove that any genus-2 Lefschetz fibration without reducible fibers and with ``transitive monodromy'' is holomorphic. The latter condition comprises all cases where the number of singular fibers is not congruent to 0 modulo 40. An auxiliary statement of independent interest is the holomorphicity of symplectic surfaces in S2-bundles over S2, of relative degree up to 7 over the base, and of symplectic surfaces in CP2 of degree up to 17.
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