## 2-spheres of square $-1$ and the geography of genus-2 Lefschetz fibrations

J. Math. Sci. Univ. Tokyo
Vol. 15 (2008), No. 4, Page 461--491.

Sato, Yoshihisa
2-spheres of square $-1$ and the geography of genus-2 Lefschetz fibrations
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.