GEOGRAPHY OF SYMPLECTIC LEFSCHETZ FIBRATIONS AND RATIONAL BLOWDOWNS


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Baykur R. I., Korkmaz M., Simone J.

Transactions of the American Mathematical Society, vol.377, no.10, pp.6771-6792, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 377 Issue: 10
  • Publication Date: 2024
  • Doi Number: 10.1090/tran/8968
  • Journal Name: Transactions of the American Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.6771-6792
  • Middle East Technical University Affiliated: Yes

Abstract

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.