Abstract
Integral symplectic 4–manifolds may be described in terms of Lefschetz fibrations. In this note we give a formula for the signature of any Lefschetz fibration in terms of the second cohomology of the moduli space of stable curves. As a consequence we see that the sphere in moduli space defined by any (not necessarily holomorphic) Lefschetz fibration has positive “symplectic volume”; it evaluates positively with the Kähler class. Some other applications of the signature formula and some more general results for genus two fibrations are discussed.
Citation
Ivan Smith. "Lefschetz fibrations and the Hodge bundle." Geom. Topol. 3 (1) 211 - 233, 1999. https://doi.org/10.2140/gt.1999.3.211
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