Symplectic 4-manifolds on the Noether line and between the Noether and half Noether lines

Sakallı, Sümeyra

doi:10.1007/s10711-021-00655-6

Cited by 2 publications

(1 citation statement)

References 27 publications

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“…The associated invariants of a compact complex surface of general type satisfy both the Bogomolov-Miayoka-Yau inequality 9χ h ≥ c 2 1 and the Noether inequality c 2 1 ≥ 2χ h − 6. Perhaps the most striking difference between the complex and symplectic geography is that the Noether inequality fails for symplectic 4-manifolds [22,14,1,41]. However, in this case, there are only sporadic examples realizing lattice points in the region 2a − 6 ≥ b > 0 as Lefschetz fibrations, which were suggested by Fintushel and Stern in [16]; see Remark 8.…”

Section: Introductionmentioning

confidence: 99%

Geography of symplectic Lefschetz fibrations and rational blowdowns

Baykur¹,

Korkmaz²,

Simone³

2022

Preprint

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We produce simply connected, minimal, symplectic Lefschetz fibrations realizing all the lattice points in the symplectic geography plane below the Noether line. This provides a symplectic extension of the classical works populating the complex geography plane with holomorphic Lefschetz fibrations. Our examples are obtained by rationally blowing down Lefschetz fibrations with clustered nodal fibers, the total spaces of which are potentially new homotopy elliptic surfaces. Similarly, clustering nodal fibers on higher genera Lefschetz fibrations on standard rational surfaces, we get rational blowdown configurations that yield new constructions of small symplectic exotic 4-manifolds. We present an example of a construction of a minimal symplectic exotic CP 2 # 5CP 2 through this procedure applied to a genus-3 fibration.

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Section: Introductionmentioning

confidence: 99%

Geography of symplectic Lefschetz fibrations and rational blowdowns

Baykur¹,

Korkmaz²,

Simone³

2022

Preprint

View full text Add to dashboard Cite

show abstract

Geography of symplectic Lefschetz fibrations and rational blowdowns

Baykur¹,

Korkmaz²,

Simone³

2024

Trans. Amer. Math. Soc.

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We produce simply-connected, minimal, symplectic Lefschetz fibrations realizing all the lattice points in the symplectic geography plane below the Noether line. This provides a symplectic extension of the classical works populating the complex geography plane with holomorphic Lefschetz fibrations. Our examples are obtained by rationally blowing down Lefschetz fibrations with clustered nodal fibers, the total spaces of which are potentially new homotopy elliptic surfaces. Similarly, clustering nodal fibers on higher genera Lefschetz fibrations on standard rational surfaces, we get rational blowdown configurations that yield new constructions of small symplectic exotic 4 4 –manifolds. We present an example of a construction of a minimal symplectic exotic C P 2 # 5 C P ¯ 2 {\mathbb {CP}}{}^{2}\# \, 5 \overline {\mathbb {CP}}{}^{2} through this procedure applied to a genus– 3 3 fibration.

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Symplectic 4-manifolds on the Noether line and between the Noether and half Noether lines

Cited by 2 publications

References 27 publications

Geography of symplectic Lefschetz fibrations and rational blowdowns

Geography of symplectic Lefschetz fibrations and rational blowdowns

Geography of symplectic Lefschetz fibrations and rational blowdowns

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