Journal of Differential Geometry

Hyperelliptic Szpiro Inequality

Fedor Bogomolov, Ludmil Katzarkov, and Tony Pantev

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.

Article information

Source
J. Differential Geom., Volume 61, Number 1 (2002), 51-80.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090351320

Digital Object Identifier
doi:10.4310/jdg/1090351320

Mathematical Reviews number (MathSciNet)
MR1949784

Zentralblatt MATH identifier
1040.14015

Citation

Bogomolov, Fedor; Katzarkov, Ludmil; Pantev, Tony. Hyperelliptic Szpiro Inequality. J. Differential Geom. 61 (2002), no. 1, 51--80. doi:10.4310/jdg/1090351320. https://projecteuclid.org/euclid.jdg/1090351320


Export citation