The ambiguity index of an equipped finite group

Fedor Bogomolov, Viktor S. Kulikov

Research output: Contribution to journalArticle

Abstract

In the paper (Kulikov in Sb Math 204(2):237–263, 2013), the ambiguity index (Formula presented.) was introduced for each equipped finite group (Formula presented.). It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group (Formula presented.) assuming that all local monodromies belong to conjugacy classes (Formula presented.) in (Formula presented.) and the number of branch points is greater than some constant. We prove in this article that the ambiguity index can be identified with the size of a generalization of so called Bogomolov multiplier (Kunyavskiĭ in Cohomological and Geometric Approaches to Rationality Problems. Progress in Mathematics, vol 282, pp 209–217, 2010), see also (Bogomolov in Math USSR-Izv 30(3):455–485, 1988) and hence can be easily computed for many pairs (Formula presented.). In particular, the ambiguity indices are completely counted in the cases when (Formula presented.) are the symmetric or alternating groups.

Original languageEnglish (US)
Pages (from-to)260-278
Number of pages19
JournalEuropean Journal of Mathematics
Volume1
Issue number2
DOIs
StatePublished - Jun 1 2015

Fingerprint

Finite Group
Hurwitz Space
Branch Point
Alternating group
Geometric Approach
Galois group
Conjugacy class
Rationality
Ambiguity
Connected Components
Symmetric group
Multiplier
Covering
Line

Keywords

  • (Formula presented.) -group
  • Bogomolov multiplier
  • Equipped group
  • Hurwitz space

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The ambiguity index of an equipped finite group. / Bogomolov, Fedor; Kulikov, Viktor S.

In: European Journal of Mathematics, Vol. 1, No. 2, 01.06.2015, p. 260-278.

Research output: Contribution to journalArticle

Bogomolov, Fedor ; Kulikov, Viktor S. / The ambiguity index of an equipped finite group. In: European Journal of Mathematics. 2015 ; Vol. 1, No. 2. pp. 260-278.
@article{8902a77b0b3248908b74e74cda5842b5,
title = "The ambiguity index of an equipped finite group",
abstract = "In the paper (Kulikov in Sb Math 204(2):237–263, 2013), the ambiguity index (Formula presented.) was introduced for each equipped finite group (Formula presented.). It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group (Formula presented.) assuming that all local monodromies belong to conjugacy classes (Formula presented.) in (Formula presented.) and the number of branch points is greater than some constant. We prove in this article that the ambiguity index can be identified with the size of a generalization of so called Bogomolov multiplier (Kunyavskiĭ in Cohomological and Geometric Approaches to Rationality Problems. Progress in Mathematics, vol 282, pp 209–217, 2010), see also (Bogomolov in Math USSR-Izv 30(3):455–485, 1988) and hence can be easily computed for many pairs (Formula presented.). In particular, the ambiguity indices are completely counted in the cases when (Formula presented.) are the symmetric or alternating groups.",
keywords = "(Formula presented.) -group, Bogomolov multiplier, Equipped group, Hurwitz space",
author = "Fedor Bogomolov and Kulikov, {Viktor S.}",
year = "2015",
month = "6",
day = "1",
doi = "10.1007/s40879-014-0015-3",
language = "English (US)",
volume = "1",
pages = "260--278",
journal = "European Journal of Mathematics",
issn = "2199-675X",
publisher = "Springer International Publishing AG",
number = "2",

}

TY - JOUR

T1 - The ambiguity index of an equipped finite group

AU - Bogomolov, Fedor

AU - Kulikov, Viktor S.

PY - 2015/6/1

Y1 - 2015/6/1

N2 - In the paper (Kulikov in Sb Math 204(2):237–263, 2013), the ambiguity index (Formula presented.) was introduced for each equipped finite group (Formula presented.). It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group (Formula presented.) assuming that all local monodromies belong to conjugacy classes (Formula presented.) in (Formula presented.) and the number of branch points is greater than some constant. We prove in this article that the ambiguity index can be identified with the size of a generalization of so called Bogomolov multiplier (Kunyavskiĭ in Cohomological and Geometric Approaches to Rationality Problems. Progress in Mathematics, vol 282, pp 209–217, 2010), see also (Bogomolov in Math USSR-Izv 30(3):455–485, 1988) and hence can be easily computed for many pairs (Formula presented.). In particular, the ambiguity indices are completely counted in the cases when (Formula presented.) are the symmetric or alternating groups.

AB - In the paper (Kulikov in Sb Math 204(2):237–263, 2013), the ambiguity index (Formula presented.) was introduced for each equipped finite group (Formula presented.). It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group (Formula presented.) assuming that all local monodromies belong to conjugacy classes (Formula presented.) in (Formula presented.) and the number of branch points is greater than some constant. We prove in this article that the ambiguity index can be identified with the size of a generalization of so called Bogomolov multiplier (Kunyavskiĭ in Cohomological and Geometric Approaches to Rationality Problems. Progress in Mathematics, vol 282, pp 209–217, 2010), see also (Bogomolov in Math USSR-Izv 30(3):455–485, 1988) and hence can be easily computed for many pairs (Formula presented.). In particular, the ambiguity indices are completely counted in the cases when (Formula presented.) are the symmetric or alternating groups.

KW - (Formula presented.) -group

KW - Bogomolov multiplier

KW - Equipped group

KW - Hurwitz space

UR - http://www.scopus.com/inward/record.url?scp=84958701399&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958701399&partnerID=8YFLogxK

U2 - 10.1007/s40879-014-0015-3

DO - 10.1007/s40879-014-0015-3

M3 - Article

VL - 1

SP - 260

EP - 278

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

IS - 2

ER -