Related papers: Toric Landau-Ginzburg models
We survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau--Ginzburg models for Fano varieties; how to apply…
In this paper we propose (0,2) mirrors for general Fano toric varieties with special tangent bundle deformations, corresponding to subsets of toric deformations. Our mirrors are of the form of (B/2-twisted) (0,2) Landau-Ginzburg models,…
Given a Fano complete intersection defined by sections of a collection nef line bundles $L_1,\ldots, L_c$ on a Fano toric manifold $Y$, a construction of Givental/Hori-Vafa provides a mirror-dual Landau-Ginzburg model. This construction…
We construct and apply Strominger-Yau-Zaslow mirror transformations to understand the geometry of the mirror symmetry between toric Fano manifolds and Landau-Ginzburg models.
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 introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in $n \leqslant 4$ variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We…
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…
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…
In 1997 Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested a construction of Landau--Ginzburg models for Fano complete intersections in Grassmannians similar to Givental's construction for complete intersections in smooth toric…
For each Fano threefold, we construct a family of Landau-Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi-Yau varieties with proper potential maps; they admit open…
We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface $H$ in a toric variety $V$ we construct…
One of the open problems in understanding (0,2) mirror symmetry concerns the construction of Toda-like Landau-Ginzburg mirrors to (0,2) theories on Fano spaces. In this paper, we begin to fill this gap by making an ansatz for (0,2)…
For an appropriate class of Fano complete intersections in toric varieties, we prove that there is a concrete relationship between degenerations to specific toric subvarieties and expressions for Givental's Landau-Ginzburg models as Laurent…
We study the behavior of toric Landau-Ginzburg models under extremal contraction and minimal model program. We also establish a relation between the moduli space of toric Landau-Ginzburg models and the geography of central models. We…
We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for…
We suggest an interpretation of mirror symmetry for toric varieties via an equivalence of two conformal field theories. The first theory is the twisted sigma model of a toric variety in the infinite volume limit (the A-model). The second…
We introduce a duality construction for toric Landau-Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau-Ginzburg model correspondence. This construction is shown to reconstruct those of…
Given a smooth log Calabi--Yau pair $(X,D)$, we use the intrinsic mirror symmetry construction to define the mirror proper Landau--Ginzburg potential and show that it is a generating function of two-point relative Gromov--Witten invariants…
Toric Landau--Ginzburg models of Givental's type for Fano complete intersections are known to have Calabi--Yau compactifications. We give an alternative proof of this fact. As an output of our proof we get a description of fibers over…
We survey on the recent progress toward mirror symmetry between Landau-Ginzburg models.