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Nonholomorphic
Lefschetz fibrations with $(-1)$-sections
Noriyuki Hamada, Ryoma Kobayashi and Naoyuki Monden |
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Vol. 298 (2019), No. 2, 375–398
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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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Authors |
| Noriyuki Hamada | |
| Department of Mathematics and
Statistics University of Massachusetts Amherst, MA United States |
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| Ryoma Kobayashi | |
| Department of General
Education Ishikawa National College of Technology Tsubata Japan |
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| Naoyuki Monden | |
| Department of Mathematics, Faculty
of Science Okayama University Okayama Japan |
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