@article{f372fd12a4994641b2257992a391065e,
title = "Nonholomorphic Lefschetz fibrations with (-1)-sections",
abstract = " We construct two types of nonholomorphic Lefschetz fibrations over S 2 with (-1)-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 nonholomorphic Lefschetz pencils without Donaldson's theorem. ",
keywords = "(-1)-sections, Complex structure, Lefschetz fibrations, Slope inequality",
author = "Noriyuki Hamada and Ryoma Kobayashi and Naoyuki Monden",
note = "Funding Information: The authors would like to thank R. Inanc Baykur for comments on this paper and for pointing out that there are more various examples of nonholomorphic Lefschetz fibrations than were mentioned in the first version of the manuscript. They are also grateful to Anar Akhmedov for comments. Finally, they are greatly indebted to the referee for invaluable comments, especially, about the proof of Theorem 1.2. Monden was supported by Grant-in-Aid for Young Scientists (B) (No. 16K17601), Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2019 Mathematical Sciences Publishers.",
year = "2019",
doi = "10.2140/pjm.2019.298.375",
language = "English",
volume = "298",
pages = "375--398",
journal = "Pacific Journal of Mathematics",
issn = "0030-8730",
publisher = "University of California, Berkeley",
number = "2",
}