2-spheres of square $-1$ and the geography of genus-2 Lefschetz fibrations
Vol. 15 (2008), No. 4, Page 461--491.
Sato, Yoshihisa
2-spheres of square $-1$ and the geography of genus-2 Lefschetz fibrations
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Abstract:
Using the Gromov invariants and the Taubes' structure theorem, we investigate how spheres of square $-1$ are embedded against fibers in relatively minimal Lefschetz fibrations over $S^2$ and show the finiteness of the geography of relatively minimal genus-2 Lefschetz fibrations containing spheres of square $-1$. Furthermore, we present the list of possible pairs $(n, s)$ of the numbers of irreducible singular fibers and reducible singular fibers in such a Lefschetz fibration.
Keywords: Lefschetz fibrations, 4-manifolds, pseudo-holomorphic curves, Gromov invariants
Mathematics Subject Classification (2000): Primary 57R17, Secondary 32Q65
Mathematical Reviews Number: MR2546906
Received: 2008-09-17
