Lefschetz fibrations and the Hodge bundle

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

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

Cited by in corpus (8)

• Lefschetz pencils and divisors in moduli space
• Surface bundles over surfaces of small genus
• Lefschetz pencils and the canonical class for symplectic 4-manifolds
• Lefschetz fibrations with small slope
• A Runge approximation theorem for pseudo-holomorphic maps
• Non-holomorphic Lefschetz fibrations with $(-1)$-sections
• Branched covers and pencils on hyperelliptic Lefschetz fibrations
• Unique fiber sum decomposability of genus 2 Lefschetz fibrations