On the holomorphicity of genus two Lefschetz fibrations

Details On the holomorphicity of genus two Lefschetz fibrations On the holomorphicity of genus two Lefschetz fibrations

2003-05-24

arxiv.org/abs/math/0305343v1

Mathematics

Symplectic Geometry

54 pp., 1 figure

Scientific paper

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 S^2-bundles over S^2, of relative degree up to 7 over the base, and of symplectic surfaces in CP^2 of degree up to 17.

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