A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities

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

Authors

  • Wolfgang Ebeling
  • David Ploog

Research Organisations

View graph of relations

Details

Original languageEnglish
Pages (from-to)195-212
Number of pages18
JournalManuscripta mathematica
Volume140
Issue number1-2
Publication statusPublished - 2013

Abstract

We consider the Berglund-Hübsch transpose of a bimodal invertible polynomial and construct a triangulated category associated to the compactification of a suitable deformation of the singularity. This is done in such a way that the corresponding Grothendieck group with the (negative) Euler form can be described by a graph which corresponds to the Coxeter-Dynkin diagram with respect to a distinguished basis of vanishing cycles of the bimodal singularity.

ASJC Scopus subject areas

Cite this

A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities. / Ebeling, Wolfgang; Ploog, David.
In: Manuscripta mathematica, Vol. 140, No. 1-2, 2013, p. 195-212.

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

Ebeling W, Ploog D. A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities. Manuscripta mathematica. 2013;140(1-2):195-212. doi: 10.1007/s00229-012-0536-3
Ebeling, Wolfgang ; Ploog, David. / A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities. In: Manuscripta mathematica. 2013 ; Vol. 140, No. 1-2. pp. 195-212.
Download
@article{d282bcb32e2e4a79a33b09c538789512,
title = "A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities",
abstract = "We consider the Berglund-H{\"u}bsch transpose of a bimodal invertible polynomial and construct a triangulated category associated to the compactification of a suitable deformation of the singularity. This is done in such a way that the corresponding Grothendieck group with the (negative) Euler form can be described by a graph which corresponds to the Coxeter-Dynkin diagram with respect to a distinguished basis of vanishing cycles of the bimodal singularity. ",
author = "Wolfgang Ebeling and David Ploog",
year = "2013",
doi = "10.1007/s00229-012-0536-3",
language = "English",
volume = "140",
pages = "195--212",
journal = "Manuscripta mathematica",
issn = "0025-2611",
publisher = "Springer New York",
number = "1-2",

}

Download

TY - JOUR

T1 - A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities

AU - Ebeling, Wolfgang

AU - Ploog, David

PY - 2013

Y1 - 2013

N2 - We consider the Berglund-Hübsch transpose of a bimodal invertible polynomial and construct a triangulated category associated to the compactification of a suitable deformation of the singularity. This is done in such a way that the corresponding Grothendieck group with the (negative) Euler form can be described by a graph which corresponds to the Coxeter-Dynkin diagram with respect to a distinguished basis of vanishing cycles of the bimodal singularity.

AB - We consider the Berglund-Hübsch transpose of a bimodal invertible polynomial and construct a triangulated category associated to the compactification of a suitable deformation of the singularity. This is done in such a way that the corresponding Grothendieck group with the (negative) Euler form can be described by a graph which corresponds to the Coxeter-Dynkin diagram with respect to a distinguished basis of vanishing cycles of the bimodal singularity.

UR - http://www.scopus.com/inward/record.url?scp=84871950194&partnerID=8YFLogxK

U2 - 10.1007/s00229-012-0536-3

DO - 10.1007/s00229-012-0536-3

M3 - Article

AN - SCOPUS:84871950194

VL - 140

SP - 195

EP - 212

JO - Manuscripta mathematica

JF - Manuscripta mathematica

SN - 0025-2611

IS - 1-2

ER -