Related papers: Mirror Symmetry via Logarithmic Degeneration Data …
We describe in detail the space of the two K\"ahler parameters of the Calabi--Yau manifold $\P_4^{(1,1,1,6,9)}[18]$ by exploiting mirror symmetry. The large complex structure limit of the mirror, which corresponds to the classical large…
This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifolds are related by the existence of dual special Lagrangian…
We study mirror symmetry of Calabi-Yau manifolds within the framework of the Gauss-Manin system. Applying the flat coordinates to the Gauss-Manin system for the periods, we derive differential equations for the mirror map in addition to the…
Fibrations of flux backgrounds by supersymmetric cycles are investigated. For an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it is argued that the product M x \hat{M} is doubly fibered by supersymmetric…
The B-side of Kontsevich's Homological Mirror Symmetry Conjecture is discussed. We give first a self-contained study of derived categories and their homological algebra, and later restrict to the bounded derived category of schemes and…
We perform the mirror transformations of Calabi-Yau manifolds with one moduli whose Hodge numbers $(h^{11}, h^{21})$ are minimally small. Since the difference of Hodge numbers is the generation of matter fields in superstring theories made…
We continue our study on the pairs of singular Calabi--Yau varieties arising from double covers over semi-Fano toric manifolds. In this paper, we first investigate singular CY double covers of \(\mathbb{P}^{3}\) branched along (1) a union…
We study the mirrors of five-parameter Calabi-Yau threefolds first studied by Hulek and Verrill in the context of observed modular behaviour of the zeta functions for Calabi-Yau manifolds. Toric geometry allows for a simple explicit…
For an arbitrary smooth n-dimensional Fano variety $X$ we introduce the notion of a small toric degeneration. Using small toric degenerations of Fano n-folds $X$, we propose a general method for constructing mirrors of Calabi-Yau complete…
The first part of this paper is a review of the Strominger-Yau-Zaslow conjecture in various settings. In particular, we summarize how, given a pair (X,D) consisting of a Kahler manifold and an anticanonical divisor, families of special…
We extend our variant of mirror symmetry for K3 surfaces \cite{GN3} and clarify its relation with mirror symmetry for Calabi-Yau manifolds. We introduce two classes (for the models A and B) of Calabi-Yau manifolds fibrated by K3 surfaces…
Motivated by Strominger-Yau-Zaslow's mirror symmetry proposal and Kontsevich's homological mirror symmetry conjecture, we study mirror phenomena (in A-model) of certain results from Donaldson-Thomas theory for Calabi-Yau 4-folds.
In the first part of the paper, we prove a mirror symmetry isomorphism between integral tropical homology groups of a pair of mirror tropical Calabi-Yau hypersurfaces. We then apply this isomorphism to prove that a primitive patchworking of…
We continue the study of the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, this states that if two Calabi-Yau manifolds X and Y are mirror partners, then X and Y have special Lagrangian torus fibrations which are dual to…
We introduce a special class of convex rational polyhedral cones which allows to construct generalized Calabi-Yau varieties of dimension $(d + 2(r-1))$, where $r$ is a positive integer and d is the dimension of critical string vacua with…
We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-K\"{a}hler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the…
Given a log Calabi-Yau surface $Y$ with maximal boundary $D$ and distinguished complex structure, we explain how to construct a mirror Lefschetz fibration $w: M \to \mathbb{C}$, where $M$ is a Weinstein four-manifold, such that the directed…
Mirror symmetry relates type IIB string theory on a Calabi-Yau 3-fold to type IIA on the mirror CY manifold, whose complex structure and Kaehler moduli spaces are exchanged. We show that the mirror map is a particular case of a more general…
We discuss mirror symmetry in generalized Calabi-Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi-Yau threefolds with NS three-form flux we show that the mirror type…
In this article, we study mirror symmetry for pairs of singular Calabi--Yau manifolds which are double covers of toric manifolds. Their period integrals can be seen as certain `fractional' analogues of those of ordinary complete…