Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98861We prove upper bounds for the number of critical points in semistable symplectic Lefschetz fibrations. We also obtain a new lower bound for the number of nonseparting vanishing cycles in Lefschetz pencils, and reprove the known lower bounds for the commutator lengths of Dehn twists.minor corrections; to appear in Trans. Amer. Math. SocSymplectic GeometryAlgebraic GeometryGeometric Topology57R17, 57R57, 14H10Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequalitytext