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Abstract
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We construct two types of nonholomorphic Lefschetz fibrations over
with
-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.
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Keywords
Lefschetz fibrations, $(-1)$-sections, slope inequality,
complex structure
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Mathematical Subject Classification 2010
Primary: 14D06, 55R55, 57R15, 57R20
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Milestones
Received: 25 December 2016
Revised: 12 April 2018
Accepted: 6 June 2018
Published: 8 March 2019
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