On the holomorphicity of genus two Lefschetz fibrations

2003/05/24 by Bernd Siebert, Gang Tian, Siebert, Bernd +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG

paper · pdf · doi:10.48550/arxiv.math/0305343

54 pp., 1 figure

arxiv created 2003/05/24 · openalex publication_date 2003/05/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds

Cited by

• A note on the topology of Lefschetz fibrations
• The Legendrian Hopf Link has exactly two Lagrangian fillings

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