Unchaining surgery and topology of symplectic 4-manifolds

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