  We study a symplectic surgery operation we call unchaining, which effectively
reduces the second Betti number and the symplectic Kodaira dimension at the
same time. Using unchaining, we give novel constructions of symplectic
Calabi-Yau surfaces from complex surfaces of general type, as well as from
rational and ruled surfaces via the natural inverse of this operation.
Combining the unchaining surgery with others, which all correspond to certain
monodromy substitutions for Lefschetz pencils, we provide further applications,
such as a complete resolution of a conjecture of Stipsicz on the existence of
exceptional sections in Lefschetz fibrations, new constructions of exotic
symplectic 4-manifolds, and inequivalent pencils of the same genera and the
same number of base points on families of symplectic 4-manifolds. Meanwhile, we
give a handy criterion for determining from the monodromy of a pencil whether
its total space is spin or not.
