We study Lefschetz pencils on symplectic four-manifolds via the associatedspheres in the moduli spaces of curves, and in particular their intersectionswith certain natural divisors. An invariant defined from such intersectionnumbers can distinguish manifolds with torsion first Chern class. We prove thatpencils of large degree always give spheres which behave `homologically' likerational curves; contrastingly, we give the first constructive example of asymplectic non-holomorphic Lefschetz pencil. We also prove that only finitelymany values of signature or Euler characteristic are realised by manifoldsadmitting Lefschetz pencils of genus two curves.
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