Details
| Original language | English |
|---|---|
| Pages (from-to) | 259-268 |
| Number of pages | 10 |
| Journal | Topology and its applications |
| Volume | 234 |
| Early online date | 24 Nov 2017 |
| Publication status | Published - 1 Feb 2018 |
Abstract
Keywords
- Braid group, Coxeter–Dynkin diagram, Distinguished basis of vanishing cycles, Intersection number, Singularity
ASJC Scopus subject areas
- Mathematics(all)
- Geometry and Topology
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In: Topology and its applications, Vol. 234, 01.02.2018, p. 259-268.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A note on distinguished bases of singularities
AU - Ebeling, Wolfgang
N1 - Funding information: Partially supported by the DFG-programme SPP1388 “Representation Theory”.
PY - 2018/2/1
Y1 - 2018/2/1
N2 - For an isolated hypersurface singularity which is neither simple nor simple elliptic, it is shown that there exists a distinguished basis of vanishing cycles which contains two basis elements with an arbitrary intersection number. This implies that the set of Coxeter–Dynkin diagrams of such a singularity is infinite, whereas it is finite for the simple and simple elliptic singularities. For the simple elliptic singularities, it is shown that the set of distinguished bases of vanishing cycles is also infinite. We also show that some of the hyperbolic unimodal singularities have Coxeter–Dynkin diagrams like the exceptional unimodal singularities.
AB - For an isolated hypersurface singularity which is neither simple nor simple elliptic, it is shown that there exists a distinguished basis of vanishing cycles which contains two basis elements with an arbitrary intersection number. This implies that the set of Coxeter–Dynkin diagrams of such a singularity is infinite, whereas it is finite for the simple and simple elliptic singularities. For the simple elliptic singularities, it is shown that the set of distinguished bases of vanishing cycles is also infinite. We also show that some of the hyperbolic unimodal singularities have Coxeter–Dynkin diagrams like the exceptional unimodal singularities.
KW - Braid group
KW - Coxeter–Dynkin diagram
KW - Distinguished basis of vanishing cycles
KW - Intersection number
KW - Singularity
UR - http://www.scopus.com/inward/record.url?scp=85035338395&partnerID=8YFLogxK
UR - https://arxiv.org/abs/1611.06074
U2 - 10.48550/arXiv.1611.06074
DO - 10.48550/arXiv.1611.06074
M3 - Article
AN - SCOPUS:85035338395
VL - 234
SP - 259
EP - 268
JO - Topology and its applications
JF - Topology and its applications
SN - 0166-8641
ER -