2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62184Let f : S --> B be a non-trivial family of semi-stable curves of genus g, N the number of critical points of f and s the number of singular fibres. We prove the inequality N < (4g+2)(s+2g(B)-2) .2 pages, Plain TeXAlgebraic Geometrytext