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"We will study a notion of Lefschetz pencils for generalized complex 4-manifolds, aiming at results analogue to those of Donalson and Gompf in symplectic geometry stating that a 4-manifold has a symplectic structure if and only if it admits a Lefschetz pencil. To achieve the desired results we have to find the right definition of a Lefschetz pencil in the generalized complex setting. Earlier work ...