Abstract
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 nonseparating vanishing cycles and the number D of singular fibers satisfy the inequality N ≤ (4g + 2)D.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 51-80 |
| Number of pages | 30 |
| Journal | Journal of Differential Geometry |
| Volume | 61 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2002 |
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology