Lefschetz fibrations and the Hodge bundle

Details Lefschetz fibrations and the Hodge bundle Lefschetz fibrations and the Hodge bundle

1999-07-14

arxiv.org/abs/math/9907200v1

Geom. Topol. 3 (1999), 211-233

Mathematics

Symplectic Geometry

23 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper9.abs.html

Scientific paper

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 Kahler class. Some other applications of the signature formula and some more general results for genus two fibrations are discussed.

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