Hyperelliptic szpiro inequality

Fedor Bogomolov, Ludmil Katzarkov, Tony Pantev

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)51-80
Number of pages30
JournalJournal of Differential Geometry
Volume61
Issue number1
DOIs
StatePublished - Jan 1 2002
Externally publishedYes

Fingerprint

Hyperelliptic Curves
Lefschetz Fibration
Vanishing Cycles
Genus
Fiber
Generalise
Family

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Hyperelliptic szpiro inequality. / Bogomolov, Fedor; Katzarkov, Ludmil; Pantev, Tony.

In: Journal of Differential Geometry, Vol. 61, No. 1, 01.01.2002, p. 51-80.

Research output: Contribution to journalArticle

Bogomolov, Fedor ; Katzarkov, Ludmil ; Pantev, Tony. / Hyperelliptic szpiro inequality. In: Journal of Differential Geometry. 2002 ; Vol. 61, No. 1. pp. 51-80.
@article{2122cb6918d548c7a936f8c2ec9ecb32,
title = "Hyperelliptic szpiro inequality",
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.",
author = "Fedor Bogomolov and Ludmil Katzarkov and Tony Pantev",
year = "2002",
month = "1",
day = "1",
doi = "10.4310/jdg/1090351320",
language = "English (US)",
volume = "61",
pages = "51--80",
journal = "Journal of Differential Geometry",
issn = "0022-040X",
publisher = "International Press of Boston, Inc.",
number = "1",

}

TY - JOUR

T1 - Hyperelliptic szpiro inequality

AU - Bogomolov, Fedor

AU - Katzarkov, Ludmil

AU - Pantev, Tony

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=57549092183&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57549092183&partnerID=8YFLogxK

U2 - 10.4310/jdg/1090351320

DO - 10.4310/jdg/1090351320

M3 - Article

AN - SCOPUS:57549092183

VL - 61

SP - 51

EP - 80

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 1

ER -