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

Abstract

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.

16 pages, 7 figures. We added some remarks and references, and minor changes in the exposition

References in corpus (2)

• The canonical pencils on Horikawa surfaces
• Lefschetz pencils and finitely presented groups

Cited by in corpus (1)

• Spin Lefschetz fibrations are abundant