Nonholomorphic Lefschetz fibrations with
(−1)-sections

Hamada, Noriyuki; Kobayashi, Ryoichi; Monden, Naoyuki

doi:10.2140/pjm.2019.298.375

Cited by 4 publications

(2 citation statements)

References 38 publications

(54 reference statements)

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“…Explicit constructions of Lefschetz fibrations with prescribed fundamental groups were given by Amorós, Bogomolov, Katzarkov and Pantev [1] and by Korkmaz [14]; also see [12]. We show that the same result holds for a much smaller family of Lefschetz fibrations: Theorem A.…”

Section: Introductionsupporting

confidence: 57%

Spin Lefschetz fibrations are abundant

Arabadji,

Baykur

2023

Pacific J. Math.

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Section: Introductionsupporting

confidence: 57%

Spin Lefschetz fibrations are abundant

Arabadji,

Baykur

2023

Pacific J. Math.

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“…While it is in general hard to obtain monodromy factorizations of Lefschetz pencils coming from Donaldson's construction, several ingenious techniques, such as fiber sum operations and substitution operations, have been employed in order to give non-holomorphic Lefschetz pencils and fibrations (on possibly non-complex four-manifolds) with explicit monodromy factorizations (e.g. [1,4,8,14,16,23,24,25]). Furthermore, Li [20] constructed non-holomorphic Lefschetz pencils on minimal Kähler surfaces of general type.…”

Section: Introductionmentioning

confidence: 99%

Topology of holomorphic Lefschetz pencils on the four-torus

Hamada

Hayano

2018

Algebr. Geom. Topol.

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In this paper we discuss topological properties of holomorphic Lefschetz pencils on the four-torus. Relying on the theory of moduli spaces of polarized abelian surfaces, we first prove that, under some mild assumption, the (smooth) isomorphism class of a holomorphic Lefschetz pencil on the four-torus is uniquely determined by its genus and divisibility. We then explicitly give a system of vanishing cycles of the genus-3 holomorphic Lefschetz pencil on the four-torus due to Smith, and obtain those of holomorphic pencils with higher genera by taking finite unbranched coverings. One can also obtain the monodromy factorization associated with Smith's pencil in a combinatorial way. This construction allows us to generalize Smith's pencil to higher genera, which is a good source of pencils on the (topological) four-torus. As another application of the combinatorial construction, for any torus bundle over the torus with a section we construct a genus-3 Lefschetz pencil whose total space is homeomorphic to that of the given bundle.

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Small exotic 4-manifolds and symplectic Calabi–Yau surfaces via genus-3 pencils

Baykur

2022

Open Book Series

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We introduce a strategy to produce exotic rational and elliptic ruled surfaces, and possibly new symplectic Calabi-Yau surfaces, via constructions of symplectic Lefschetz pencils using a novel technique we call breeding. We deploy our strategy to breed explicit symplectic genus-3 pencils, whose total spaces are homeomorphic but not diffeomorphic to the rational surfaces ‫ސރ‬ 2 # ‫ސރ‪p‬‬ 2 for p = 6, 7, 8, 9. Similarly, we breed explicit genus-3 pencils, whose total spaces are symplectic Calabi-Yau surfaces that have b 1 > 0 and realize all the integral homology classes of torus bundles over tori.

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Nonholomorphic Lefschetz fibrations with (−1)-sections

Cited by 4 publications

References 38 publications

Spin Lefschetz fibrations are abundant

Spin Lefschetz fibrations are abundant

Topology of holomorphic Lefschetz pencils on the four-torus

Small exotic 4-manifolds and symplectic Calabi–Yau surfaces via genus-3 pencils

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