GEOGRAPHY OF SYMPLECTIC LEFSCHETZ FIBRATIONS AND RATIONAL BLOWDOWNS

Date

2024-10-01

Author

Baykur, R. Inanç
Korkmaz, Mustafa
Simone, Jonathan

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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 CP2# 5CP2 through this procedure applied to a genus–3 fibration.

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https://hdl.handle.net/11511/112226

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Department of Mathematics, Article