Non-holomorphic Lefschetz fibrations with $(-1)$-sections
Geometric Topology
2019-04-10 v2 Symplectic Geometry
Abstract
We construct two types of non-holomorphic Lefschetz fibrations over with -sections ---hence, they are fiber sum indecomposable--- by giving the corresponding positive relators. One type of the two does not satisfy the slope inequality (a necessary condition for a fibration to be holomorphic) and has a simply-connected total space, and the other has a total space that cannot admit any complex structure in the first place. These give an alternative existence proof for non-holomorphic Lefschetz pencils without Donaldson's theorem.
Cite
@article{arxiv.1609.02420,
title = {Non-holomorphic Lefschetz fibrations with $(-1)$-sections},
author = {Noriyuki Hamada and Ryoma Kobayashi and Naoyuki Monden},
journal= {arXiv preprint arXiv:1609.02420},
year = {2019}
}
Comments
16 pages, 7 figures. We added some remarks and references, and minor changes in the exposition