On the holomorphicity of genus two Lefschetz fibrations
Symplectic Geometry
2007-05-23 v1
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 S^2-bundles over S^2, of relative degree up to 7 over the base, and of symplectic surfaces in CP^2 of degree up to 17.
Cite
@article{arxiv.math/0305343,
title = {On the holomorphicity of genus two Lefschetz fibrations},
author = {Bernd Siebert and Gang Tian},
journal= {arXiv preprint arXiv:math/0305343},
year = {2007}
}
Comments
54 pp., 1 figure