Periods of the multiple Berglund-Huebsch-Krawitz mirrors

Hori-Vafa mirror periods, Picard-Fuchs equations, and Berglund-Hübsch-Krawitz duality

This paper discusses the overlap of the Hori-Vafa formulation of mirror symmetry with some other constructions. We focus on compact Calabi-Yau hypersurfaces \mathcal{M}_G = {G = 0} in weighted complex projective spaces. The Hori-Vafa formalism relates a family {\mathcal{M}_G \in WCP^{m-1}_{Q_1,...,Q_m}[s] | \sum_{i=1}^m Q_i = s} of such hypersurfaces to a single Landau-Ginzburg mirror theory. A technique suggested by Hori and Vafa allows the Picard-Fuchs equations satisfied by the corresponding mirror periods to be determined. Some examples in which the variety \mathcal{M}_G is crepantly resol…

Derived Categories of BHK Mirrors

We prove a derived analogue to the results of Borisov, Clarke, Kelly, and Shoemaker on the birationality of Berglund-Hubsch-Krawitz mirrors. Heavily bootstrapping off work of Seidel and Sheridan, we obtain Homological Mirror Symmetry for Berglund-Hubsch-Krawitz mirror pencils to hypersurfaces in projective space.

LG/CY correspondence: the state space isomorphism

We prove the classical mirror symmetry conjecture for the mirror pairs constructed by Berglund, Hübsch, and Krawitz. Our main tool is a cohomological LG/CY correspondence which provides a degree-preserving isomorphism between the cohomology of finite quotients of Calabi-Yau hypersurfaces inside a weighted projective space and the Fan-Jarvis-Ruan-Witten state space of the associated Landau-Ginzburg singularity theory.

The mirror symmetry of K3 surfaces with non-symplectic automorphisms of prime order

We consider K3 surfaces that possess certain automorphisms of prime order p>2 and we present, for these surfaces, a correspondence between the mirror symmetry of Berglund-Huebsch-Chiodo-Ruan and that for lattice polarized K3 surfaces presented by Dolgachev.

On the equivalence of Batyrev and BHK Mirror symmetry constructions

We consider the connection between two constructions of the mirror partner for the Calabi-Yau orbifold. This orbifold is defined as a quotient by some suitable subgroup $G$ of the phase symmetries of the hypersurface $ X_M $ in the weighted projective space, cut out by a quasi-homogeneous polynomial $W_M$. The first, Berglund-Hübsch-Krawitz (BHK) construction, uses another weighted projective space and the quotient of a new hypersurface $X_{M^T}$ inside it by some dual group $G^T$. In the second, Batyrev construction, the mirror partner is constructed as a hypersurface in the toric variety def…

Berglund-Hubsch Calabi-Yau轨形及其环型多项式镜像对的构造

Construction of mirror pairs of Berglund-Hubsch Calabi-Yau orbifolds of loop-type polynomials

本文提出构造BHK型Calabi-Yau轨形及其镜像对的算法，枚举216个环型多项式，发现两个构型具有三代夸克和轻子，对粒子物理模型构建有重要意义。