Related papers: A Landau-Ginzburg mirror theorem via matrix factor…
We consider the Berglund-H\"ubsch-Henningson-Takahashi duality of Landau-Ginzburg orbifolds with a symmetry group generated by some diagonal symmetries and some permutations of variables. We study the orbifold Euler characteristics, the…
In this article, we establish homological Berglund--H\"ubsch mirror symmetry for curve singularities where the A--model incorporates equivariance, otherwise known as homological Berglund--H\"ubsch--Henningson mirror symmetry, including for…
In this paper we prove the smoothness of the moduli space of Landau-Ginzburg models. We formulate and prove a Tian-Todorov theorem for the deformations of Landau-Ginzburg models, develop the necessary Hodge theory for varieties with…
In this paper, we will describe the mathematical foundation of topological Landau-Ginzburg (LG) models coupled to gravity at genus 0 in terms of primitive forms. We also discuss the mirror symmetry for Calabi-Yau manifolds and CP^1 in our…
We investigate a potential relationship between mirror symmetry for Calabi-Yau manifolds and the mirror duality between quasi-Fano varieties and Landau-Ginzburg models. More precisely, we show that if a Calabi-Yau admits a so-called Tyurin…
We construct dual descriptions of (0,2) gauged linear sigma models. In some cases, the dual is a (0,2) Landau-Ginzburg theory, while in other cases, it is a non-linear sigma model. The duality map defines an analogue of mirror symmetry for…
We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the Gamma-class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for…
In this paper we define an equivariant Floer $A_\infty$ algebra for $\mathbb{C}$ and $\mathbb{C} P^1$ by using Cartan model. We then prove an equivariant homological mirror symmetry, i.e. an equivalence between an $A_\infty$ category of…
We present an algorithm for determining all inequivalent abelian symmetries of non-degenerate quasi-homogeneous polynomials and apply it to the recently constructed complete set of Landau--Ginzburg potentials for $N=2$ superconformal field…
We give a survey on results related to the Berglund-H\"ubsch duality of invertible polynomials and the homological mirror symmetry conjecture for singularities.
We classify when the blowup of a complex Grassmannian $G(k, n)$ along a smooth Schubert subvariety $Z$ is Fano. We compute almost all the two-point, genus zero Gromov-Witten invariants of the blowup when $Z=G(k, n-1)$. We further prove a…
We use a recent classification of non-degenerate quasihomogeneous polynomials to construct all Landau-Ginzburg (LG) potentials for N=2 superconformal field theories with c=9 and calculate the corresponding Hodge numbers. Surprisingly, the…
The present paper is dedicated to illustrating an extension of polar duality between Fano toric varieties to a more general duality, called \emph{framed} duality, so giving rise to a powerful and unified method of producing mirror partners…
Mirror symmetry predicts that bounded derived category of a smooth Fano variety is equivalent to Fukaya-Seidel category of its Landau-Ginzburg model. It is expected that fibers of Landau-Ginzburg model with ordinary double points correspond…
We give a new proof of Givental's mirror theorem for toric manifolds using shift operators of equivariant parameters. The proof is almost tautological: it gives an A-model construction of the I-function and the mirror map. It also works for…
We describe the tropical mirror for complex toric surfaces. In particular we provide an explicit expression for the mirror states and show that they can be written in enumerative form. Their holomorphic germs give an explicit form of good…
We study Landau-Ginzburg orbifolds $(f,G)$ with $f=x_1^n+\ldots+x_N^n$ and $G=S\ltimes G^d$, where $S\subseteq S_N$ and $G^d$ is either the maximal group of scalar symmetries of $f$ or the intersection of the maximal diagonal symmetries of…
We study matrix factorizations of a section W of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity…
This is a sequel to our paper arXiv:2008.13462, where we proposed a definition of the Morse homotopy of the moment polytope of toric manifolds. Using this as the substitute of the Fukaya category of the toric manifolds, we proved a version…
In mirror symmetry, symplectic Landau-Ginzburg models are mirror to a large class of examples, in particular to Fano varieties and hypersurfaces of many Calabi-Yau and Fano varieties. When studying their Fukaya categories on the A-model in…