On the holomorphicity of genus two Lefschetz fibrations

• 成果类型: Article
• 署名作者: Siebert, B; Tian, G
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.161.959
• 发表日期: 2005
• 页码: 959-1020
• 关键词: surfaces; pencils; CURVES

摘要

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 mu is an element of 10 N 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 CP2 of degree <= 17.