Lefschetz fibrations and the Hodge bundle
نویسندگان
چکیده
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. AMS Classification numbers Primary: 53C15 Secondary: 53C55, 58F99
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