Non-holomorphic Lefschetz fibrations with \((-1)\)-sections

We construct two types of non-holomorphic 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 holo...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2016-10
Main Authors: Hamada, Noriyuki, Kobayashi, Ryoma, Monden, Naoyuki
Format: Article
Language:English
Subjects:
Existence theorems
Mathematical analysis
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We construct two types of non-holomorphic 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 non-holomorphic Lefschetz pencils without Donaldson's theorem.
ISSN:2331-8422
DOI:10.48550/arxiv.1609.02420