Related papers: A proposal for (0,2) mirrors of toric varieties
In the class of (0,2) heterotic compactifications which has been constructed in the framework of gauged linear sigma models the Calabi-Yau varieties X are realized as complete intersections of hypersurfaces in toric varieties IP and the…
For all punctured Riemann surfaces arising as mirror curves of toric Calabi--Yau threefolds, we show that their symplectic cohomology is isomorphic to the compactly supported Hochschild cohomology of the noncommutative Landau--Ginzburg…
We develop some ideas of Morrison and Plesser and formulate a precise mathematical conjecture which has close relations to toric mirror symmetry. Our conjecture, we call it Toric Residue Mirror Conjecture, claims that the generating…
In this paper, we give a tropical method for computing Gromov-Witten type invariants of Fano manifolds of special type. This method applies to those Fano manifolds which admit toric degenerations to toric Fano varieties with singularities…
We describe a practical and effective method for reconstructing the deformation class of a Fano manifold X from a Laurent polynomial f that corresponds to X under Mirror Symmetry. We explore connections to nef partitions, the smoothing of…
We continue our study of equivariant local mirror symmetry of curves, i.e. mirror symmetry for X_k=O(k)+O(-2-k) over P^1 with torus action (lambda_1,lambda_2) on the bundle. For the antidiagonal action lambda_1=-lambda_2, we find closed…
We introduce a class of Laurent polynomials, called maximally mutable Laurent polynomials (MMLPs), that we believe correspond under mirror symmetry to Fano varieties. A subclass of these, called rigid, are expected to correspond to Fano…
In this paper we give an inherently toric description of a special class of sheaves (known as equivariant sheaves) over toric varieties, due in part to A. A. Klyachko. We apply this technology to heterotic compactifications, in particular…
We study Landau Ginzburg (LG) theories mirror to 2D N=2 gauged linear sigma models on toric Calabi-Yau manifolds. We derive and solve new constraint equations for Landau Ginzburg elliptic Calabi-Yau superpotentials, depending on the…
Firstly, we see that the bases of the miniversal deformations of isolated $\mathbb{Q}$-Gorenstein toric singularities are quite restricted. In particular, we classify the analytic germs of embedding dimension $\leq 2$ which are the bases of…
We describe the tropical curves in toric varieties and define the tropical Gromov-Witten invariants. We introduce amplitudes for the higher topological quantum mechanics (HTQM) on special trees and show that the amplitudes are equal to the…
We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form $X=\mathbb{P}(K_Y\oplus\mathcal{O}_Y)$, where $Y$ is a toric Fano manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of $X$. As…
Hille and Perling associate to every cyclic full strongly exceptional sequence of line bundles on a toric weak Fano surface a toric system, which defines a new toric surface. In this note we interprete this construction as an instance of…
We investigate mirror symmetry for toric Calabi-Yau manifolds from the perspective of the SYZ conjecture. Starting with a non-toric special Lagrangian torus fibration on a toric Calabi-Yau manifold $X$, we construct a complex manifold…
Given a smooth toric variety X and an ample line bundle O(1), we construct a sequence of Lagrangian submanifolds of (C^*)^n with boundary on a level set of the Landau-Ginzburg mirror of X. The corresponding Floer homology groups form a…
We present here the K-theoretic version of mirror models of toric manifold. First, we recall the construction of cohomological mirrors for toric manifolds, i.e. representations of the toric hypergeometric functions from quantum cohomology…
Using mirror pairs (M_3, W_3) in type II superstring compactifications on Calabi-Yau threefolds, we study, geometrically, F-theory duals of M-theory on seven manifolds with G_2 holonomy. We first develop a way for getting Landau Ginzburg…
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…
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…
We study mirror symmetry of type II strings on manifolds with the exceptional holonomy groups $G_2$ and Spin(7). Our central result is a construction of mirrors of Spin(7) manifolds realized as generalized connected sums. In parallel to…