Hyperelliptic szpiro inequality

Fedor Bogomolov, Ludmil Katzarkov, Tony Pantev

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)51-80
Number of pages30
JournalJournal of Differential Geometry
Issue number1
StatePublished - 2002

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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