Poincaré series and Coxeter functors for Fuchsian singularities

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autorschaft

  • Wolfgang Ebeling
  • David Ploog

Organisationseinheiten

Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)1387-1398
Seitenumfang12
FachzeitschriftAdvances in Mathematics
Jahrgang225
Ausgabenummer3
PublikationsstatusVeröffentlicht - Okt. 2010

Abstract

We consider Fuchsian singularities of arbitrary genus and prove, in a conceptual manner, a formula for their Poincaré series. This uses Coxeter elements involving Eichler-Siegel transformations. We give geometrical interpretations for the lattices and isometries involved, lifting them to triangulated categories.

ASJC Scopus Sachgebiete

Zitieren

Poincaré series and Coxeter functors for Fuchsian singularities. / Ebeling, Wolfgang; Ploog, David.
in: Advances in Mathematics, Jahrgang 225, Nr. 3, 10.2010, S. 1387-1398.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Ebeling W, Ploog D. Poincaré series and Coxeter functors for Fuchsian singularities. Advances in Mathematics. 2010 Okt;225(3):1387-1398. doi: 10.1016/j.aim.2010.03.030
Ebeling, Wolfgang ; Ploog, David. / Poincaré series and Coxeter functors for Fuchsian singularities. in: Advances in Mathematics. 2010 ; Jahrgang 225, Nr. 3. S. 1387-1398.
Download
@article{d26f2b50608741f4b32e2b9f516eee04,
title = "Poincar{\'e} series and Coxeter functors for Fuchsian singularities",
abstract = "We consider Fuchsian singularities of arbitrary genus and prove, in a conceptual manner, a formula for their Poincar{\'e} series. This uses Coxeter elements involving Eichler-Siegel transformations. We give geometrical interpretations for the lattices and isometries involved, lifting them to triangulated categories. ",
keywords = "Coxeter element, Eichler-Siegel transformation, Poincar{\'e} series, Spherical twist functor",
author = "Wolfgang Ebeling and David Ploog",
note = "Funding Information: ✩ Supported by the DFG-programme “Representation Theory” (Eb 102/6-1). The second author likes to thank the DFG whose grant allowed him to enjoy the hospitality of the University of Toronto. * Corresponding author. E-mail addresses: ebeling@math.uni-hannover.de (W. Ebeling), ploog@math.uni-hannover.de (D. Ploog). Copyright: Copyright 2010 Elsevier B.V., All rights reserved.",
year = "2010",
month = oct,
doi = "10.1016/j.aim.2010.03.030",
language = "English",
volume = "225",
pages = "1387--1398",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
number = "3",

}

Download

TY - JOUR

T1 - Poincaré series and Coxeter functors for Fuchsian singularities

AU - Ebeling, Wolfgang

AU - Ploog, David

N1 - Funding Information: ✩ Supported by the DFG-programme “Representation Theory” (Eb 102/6-1). The second author likes to thank the DFG whose grant allowed him to enjoy the hospitality of the University of Toronto. * Corresponding author. E-mail addresses: ebeling@math.uni-hannover.de (W. Ebeling), ploog@math.uni-hannover.de (D. Ploog). Copyright: Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010/10

Y1 - 2010/10

N2 - We consider Fuchsian singularities of arbitrary genus and prove, in a conceptual manner, a formula for their Poincaré series. This uses Coxeter elements involving Eichler-Siegel transformations. We give geometrical interpretations for the lattices and isometries involved, lifting them to triangulated categories.

AB - We consider Fuchsian singularities of arbitrary genus and prove, in a conceptual manner, a formula for their Poincaré series. This uses Coxeter elements involving Eichler-Siegel transformations. We give geometrical interpretations for the lattices and isometries involved, lifting them to triangulated categories.

KW - Coxeter element

KW - Eichler-Siegel transformation

KW - Poincaré series

KW - Spherical twist functor

UR - http://www.scopus.com/inward/record.url?scp=77955847138&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2010.03.030

DO - 10.1016/j.aim.2010.03.030

M3 - Article

AN - SCOPUS:77955847138

VL - 225

SP - 1387

EP - 1398

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 3

ER -