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 μ, ∈ 10ℕ is not congruent to 0 modulo 40. This proves a conjecture of the authors in [SiTil]. An auxiliary statement of independent interest is the holomorphicity of symplectic surfaces in S2-bundles over S2, of relative degree ≤ 7 over the base, and of symplectic surfaces in ℂℙ 2 of degree ≤ 17.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty