Density of monodromy actions on non-abelian cohomology

Ludmil Katzarkov, Tony Pantev, Carlos Simpson

Research output: Contribution to journalArticle

Abstract

In this paper we study the monodromy action on the first Betti and de Rham non-Abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski-dense monodromy orbit. In particular, we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense.

Original languageEnglish (US)
Pages (from-to)155-204
Number of pages50
JournalAdvances in Mathematics
Volume179
Issue number2
DOIs
StatePublished - Nov 10 2003
Externally publishedYes

Fingerprint

Non-abelian Cohomology
Monodromy
De Rham Cohomology
Orbit
Curve
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Density of monodromy actions on non-abelian cohomology. / Katzarkov, Ludmil; Pantev, Tony; Simpson, Carlos.

In: Advances in Mathematics, Vol. 179, No. 2, 10.11.2003, p. 155-204.

Research output: Contribution to journalArticle

Katzarkov, Ludmil ; Pantev, Tony ; Simpson, Carlos. / Density of monodromy actions on non-abelian cohomology. In: Advances in Mathematics. 2003 ; Vol. 179, No. 2. pp. 155-204.
@article{49a6081a3aa544a89758802d16d8cd41,
title = "Density of monodromy actions on non-abelian cohomology",
abstract = "In this paper we study the monodromy action on the first Betti and de Rham non-Abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski-dense monodromy orbit. In particular, we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense.",
author = "Ludmil Katzarkov and Tony Pantev and Carlos Simpson",
year = "2003",
month = "11",
day = "10",
doi = "10.1016/S0001-8708(02)00070-1",
language = "English (US)",
volume = "179",
pages = "155--204",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Density of monodromy actions on non-abelian cohomology

AU - Katzarkov, Ludmil

AU - Pantev, Tony

AU - Simpson, Carlos

PY - 2003/11/10

Y1 - 2003/11/10

N2 - In this paper we study the monodromy action on the first Betti and de Rham non-Abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski-dense monodromy orbit. In particular, we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense.

AB - In this paper we study the monodromy action on the first Betti and de Rham non-Abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski-dense monodromy orbit. In particular, we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense.

UR - http://www.scopus.com/inward/record.url?scp=0242427709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242427709&partnerID=8YFLogxK

U2 - 10.1016/S0001-8708(02)00070-1

DO - 10.1016/S0001-8708(02)00070-1

M3 - Article

VL - 179

SP - 155

EP - 204

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -