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We prove upper bounds for the number of critical points in semistablesymplectic Lefschetz fibrations. We also obtain a new lower bound for thenumber of nonseparting vanishing cycles in Lefschetz pencils, and reprove theknown lower bounds for the commutator lengths of Dehn twists.Comment: minor corrections; to appear in Trans. Amer. Math. So

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