On the holomorphicity of genus two Lefschetz fibrations

Bernd Siebert, Gang Tian

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42 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)959-1020
Number of pages62
JournalAnnals of Mathematics
Issue number2
StatePublished - Mar 2005

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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