Closed Groups of Automorphisms of Products of Hyperbolic Riemann Surfaces

Evgeny A. Poletsky; Sergey E. Sharonov

doi:10.1007/s12220-017-9972-3

Closed Groups of Automorphisms of Products of Hyperbolic Riemann Surfaces

Evgeny A. Poletsky, Sergey E. Sharonov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we provide the complete list of all closed groups G of automorphisms of a product R of hyperbolic Riemann surfaces such that the order of any element in G/ G_e, where G_e is the identity component of G, is finite. In particular, if X is an analytic subvariety of R then the identity component of the stabilizer of X in Aut R is on this list. In its turn, it allows us to state that the identity component of the group Aut X must contain a group from this list.

Original language	English (US)
Pages (from-to)	3690-3707
Number of pages	18
Journal	Journal of Geometric Analysis
Volume	28
Issue number	4
DOIs	https://doi.org/10.1007/s12220-017-9972-3
State	Published - Dec 15 2018

Keywords

Automorphisms of complex manifolds
Exponential Lie groups
Non-discrete subgroups
Stabilizers

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s12220-017-9972-3

Cite this

@article{965527f783ed47d88f96a94d8033fb73,

title = "Closed Groups of Automorphisms of Products of Hyperbolic Riemann Surfaces",

abstract = "In this paper, we provide the complete list of all closed groups G of automorphisms of a product R of hyperbolic Riemann surfaces such that the order of any element in G/ Ge, where Ge is the identity component of G, is finite. In particular, if X is an analytic subvariety of R then the identity component of the stabilizer of X in Aut R is on this list. In its turn, it allows us to state that the identity component of the group Aut X must contain a group from this list.",

keywords = "Automorphisms of complex manifolds, Exponential Lie groups, Non-discrete subgroups, Stabilizers",

author = "Poletsky, {Evgeny A.} and Sharonov, {Sergey E.}",

note = "Funding Information: Evgeny A. Poletsky was partially supported by a grant from Simons Foundation. Publisher Copyright: {\textcopyright} 2017, Mathematica Josephina, Inc.",

year = "2018",

month = dec,

day = "15",

doi = "10.1007/s12220-017-9972-3",

language = "English (US)",

volume = "28",

pages = "3690--3707",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - Closed Groups of Automorphisms of Products of Hyperbolic Riemann Surfaces

AU - Poletsky, Evgeny A.

AU - Sharonov, Sergey E.

PY - 2018/12/15

Y1 - 2018/12/15

N2 - In this paper, we provide the complete list of all closed groups G of automorphisms of a product R of hyperbolic Riemann surfaces such that the order of any element in G/ Ge, where Ge is the identity component of G, is finite. In particular, if X is an analytic subvariety of R then the identity component of the stabilizer of X in Aut R is on this list. In its turn, it allows us to state that the identity component of the group Aut X must contain a group from this list.

AB - In this paper, we provide the complete list of all closed groups G of automorphisms of a product R of hyperbolic Riemann surfaces such that the order of any element in G/ Ge, where Ge is the identity component of G, is finite. In particular, if X is an analytic subvariety of R then the identity component of the stabilizer of X in Aut R is on this list. In its turn, it allows us to state that the identity component of the group Aut X must contain a group from this list.

KW - Automorphisms of complex manifolds

KW - Exponential Lie groups

KW - Non-discrete subgroups

KW - Stabilizers

UR - http://www.scopus.com/inward/record.url?scp=85037686326&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037686326&partnerID=8YFLogxK

U2 - 10.1007/s12220-017-9972-3

DO - 10.1007/s12220-017-9972-3

M3 - Article

AN - SCOPUS:85037686326

SN - 1050-6926

VL - 28

SP - 3690

EP - 3707

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 4

ER -

Closed Groups of Automorphisms of Products of Hyperbolic Riemann Surfaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this