#### Vol. 298, No. 2, 2019

 Recent Issues Vol. 305: 1  2 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Vol. 299: 1  2 Vol. 298: 1  2 Online Archive Volume: Issue:
 The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals
Nonholomorphic Lefschetz fibrations with $(-1)$-sections

### Noriyuki Hamada, Ryoma Kobayashi and Naoyuki Monden

Vol. 298 (2019), No. 2, 375–398
##### Abstract

We construct two types of nonholomorphic Lefschetz fibrations over ${S}^{2}$ with $\left(-1\right)$-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
Lefschetz fibrations, $(-1)$-sections, slope inequality, complex structure
##### Mathematical Subject Classification 2010
Primary: 14D06, 55R55, 57R15, 57R20