2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61726We generalize the classical Szpiro inequality to the case of a semistable family of hyperelliptic curves. We show that for a semistable symplectic Lefschetz fibration of hyperelliptic curves of genus $g$, the number $N$ of non-separating vanishing cycles and the number $D$ of singular fibers satisfy the inequality $N \leq (4g+2)D$.LaTeX2e, 27 pagesGeometric TopologyAlgebraic Geometrytext