# Simple Elliptic Singularities: a note on their G-function

@article{Strachan2010SimpleES, title={Simple Elliptic Singularities: a note on their G-function}, author={Ian A. B. Strachan}, journal={arXiv: Mathematical Physics}, year={2010} }

The link between Frobenius manifolds and singularity theory is well known, with the simplest examples coming from the simple hypersurface singularities. Associated with any such manifold is a function known as the $G$-function. This plays a role in the construction of higher-genus terms in various theories. For the simple singularities the G-function is known explicitly: G=0. The next class of singularities, the unimodal hypersurface or elliptic hypersurface singularities consists of three…

## 9 Citations

Gromov-Witten theory of elliptic orbifold P^1 and quasi-modular forms

- Mathematics
- 2011

In this paper we prove that the GW invariants of the elliptic orbifold lines with weights (3,3,3), (4,4,2), and (6,3,2) are quasi-modular forms. Our method is based on Givental's higher genus…

Modular Frobenius manifolds and their invariant flows

- Mathematics, Physics
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The space of Frobenius manifolds has a natural involutive symmetry on it: there exists a map $I$ which send a Frobenius manifold to another Frobenius manifold. Also, from a Frobenius manifold one may…

Polynomial modular Frobenius manifolds

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The moduli space of Frobenius manifolds carries a natural involutive symmetry, and a distinguished class–so-called modular Frobenius manifolds–lie at the fixed points of this symmetry. In this paper…

Gromov--Witten invariants for mirror orbifolds of simple elliptic singularities

- Mathematics, Physics
- 2011

We consider a mirror symmetry of simple elliptic singularities. In particular, we construct isomorphisms of Frobenius manifolds among the one from the Gromov--Witten theory of a weighted projective…

A new construction of $\tilde{D}_5$-singularities and generalization of Slodowy slices

- Mathematics
- 2012

Any simple elliptic singularity of type $\tilde{D}_5$ can be obtained by taking the intersection of the nilpotent variety and the 4-dimensional "good slices" in the semi-simple Lie algebra ${\frak…

Landau-Ginzburg/Calabi-Yau Correspondence of all Genera for Elliptic Orbifold $\mathbb{p}^1$

- Mathematics, Physics
- 2011

In this paper, we establish the convergence for Gromov-Witten invariant of elliptic orbifold $\mathbb{P}^1$ with type $(3,3,3), (4,4,2)$ and $(6,3,2)$. We also prove the mirror theorems of…

Strong Convergence of Euler Approximations of Stochastic Differential Equations with Delay under Local Lipschitz Condition

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For each del Pezzo surface S with du Val singularities, we determine whether it admits a (−KS)-polar cylinder or not. If it allows one, then we present an effective Q-divisor D that is Q-linearly…

Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms

- Mathematics, Physics
- 2021

We study one-parameter deformations of Calabi-Yau type Fermat polynomial singularities along degree-one directions. We show that twisted sectors in the vanishing cohomology are components of…

Higher Genus FJRW Theory for Fermat Cubic Singularity

- MathematicsActa Mathematica Sinica, English Series
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In this paper, we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Givental formalism. As results, we prove the finite generation…

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In this paper we prove that the GW invariants of the elliptic orbifold lines with weights (3,3,3), (4,4,2), and (6,3,2) are quasi-modular forms. Our method is based on Givental's higher genus…

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The space of Frobenius manifolds has a natural involutive symmetry on it: there exists a map $I$ which send a Frobenius manifold to another Frobenius manifold. Also, from a Frobenius manifold one may…

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