On the holomorphicity of genus two Lefschetz fibrations

By Bernd S Siebert, G. Tian. 2003

97 citations recorded by the source corpus.

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 [SiTi1]. An auxiliary statement of independent interest is the holomorphicity of symplectic surfaces in S 2 -bundles over S 2 , of relative degree ≤ 7 over the base, and of symplectic surfaces in CP 2 of degree ≤ 17.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c615dbbf26eccbc3f006a23c09639acdf93590df

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In Geometry and Topology

1. R. Fintushel
2. Ronald J. Stern
3. Anar Akhmedov
4. R. Baykur
5. B. Park
6. Jonathan Rosenberg
7. Doug Park

In Mathematical Physics

1. R. Fintushel
2. Ronald J. Stern
3. Anar Akhmedov

Citations in the corpus

• Six Lectures on Four 4-Manifolds (2006, background): “This is precisely the situation covered by the work of Siebert and Tian [47] which guarantees that any two such symplectic curves in S(2) × S(2) are isotopic.”