The Szpiro inequality for higher genus fibrations

Abstract

Let 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 TeX

References in corpus (1)

• The minimal number of singular fibers of a semistable curves over P^1

Cited by in corpus (2)

• Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality
• Comments on Arithmetic Teichmuller Spaces