Mirror symmetry between orbifold curves and cusp singularities with group action
By W. Ebeling, A. Takahashi. 2011
48 citations recorded by the source corpus.
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-H\"ubsch 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.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3646fbf7d3d6ff195578003ad18940c55f03f876
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In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Triangle singularities, ADE-chains, and weighted projective lines (2012, background): “This latter aspect, in particular, includes the aspects of strange duality [13, 14] and mirror symmetry [12, 70].”
- Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c} (2013, methodology): “n [MR], Krawitz-Shen [KS] and MilanovShen [MS]. Another half of homological mirror symmetry for weighted projective lines P1 a;b;c was formulated by Takahashi [Tak10] and studied by Ebeling-Takahashi [ET13], Ueda [Ued] and Keating [Kea]. Namely derived categories of weighted projective lines should ”