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

Noriyuki Hamada; Ryoma Kobayashi; Naoyuki Monden

doi:10.2140/pjm.2019.298.375

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arXiv · 1609.02420

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

Noriyuki Hamada·Ryoma Kobayashi·Naoyuki Monden

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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.

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Noriyuki Hamada, Ryoma Kobayashi, Naoyuki Monden. 2016-09-08. Non-holomorphic Lefschetz fibrations with $(-1)$-sections. https://doi.org/10.2140/pjm.2019.298.375

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