Details
| Original language | English |
|---|---|
| Pages (from-to) | 2240-2270 |
| Number of pages | 31 |
| Journal | International Mathematics Research Notices |
| Volume | 2013 |
| Issue number | 10 |
| Publication status | Published - 2013 |
Abstract
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: International Mathematics Research Notices, Vol. 2013, No. 10, 2013, p. 2240-2270.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Mirror symmetry between orbifold curves and cusp singularities with group action
AU - Ebeling, Wolfgang
AU - Takahashi, Atsushi
N1 - Funding information: This work was supported by the DFG-programme SPP 1388 ”Representation Theory” (Eb 102/6-1). The second author was also supported by Grant-in Aid for Scientific Research grant numbers 20360043 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
PY - 2013
Y1 - 2013
N2 - We consider an orbifold Landau-Ginzburg model $(f,G)$, where $f$ is an invertible polynomial in three variables and $G$ a finite group of symmetries of $f$ containing the exponential grading operator, and its Berglund-Hübsch transpose $(f^T, G^T)$. We show that this defines a mirror symmetry between orbifold curves and cusp singularities with group action. We define Dolgachev numbers for the orbifold curves and Gabrielov numbers for the cusp singularities with group action. We show that these numbers are the same and that the stringy Euler number of the orbifold curve coincides with the $G^T$-equivariant Milnor number of the mirror cusp singularity.
AB - We consider an orbifold Landau-Ginzburg model $(f,G)$, where $f$ is an invertible polynomial in three variables and $G$ a finite group of symmetries of $f$ containing the exponential grading operator, and its Berglund-Hübsch transpose $(f^T, G^T)$. We show that this defines a mirror symmetry between orbifold curves and cusp singularities with group action. We define Dolgachev numbers for the orbifold curves and Gabrielov numbers for the cusp singularities with group action. We show that these numbers are the same and that the stringy Euler number of the orbifold curve coincides with the $G^T$-equivariant Milnor number of the mirror cusp singularity.
UR - http://www.scopus.com/inward/record.url?scp=84878079144&partnerID=8YFLogxK
UR - https://arxiv.org/abs/1103.5367
U2 - 10.1093/imrn/rns115
DO - 10.1093/imrn/rns115
M3 - Article
AN - SCOPUS:84878079144
VL - 2013
SP - 2240
EP - 2270
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 10
ER -