Hyperelliptic Szpiro inequality

Details Hyperelliptic Szpiro inequality Hyperelliptic Szpiro inequality

2001-06-25

arxiv.org/abs/math/0106212v1

Mathematics

Geometric Topology

LaTeX2e, 27 pages

Scientific paper

We 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 $N \leq (4g+2)D$.

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