Related papers: Mirror symmetry and self-dual manifolds
Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a…
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…
We study the geometry of singular $\text{SL}_n$-Hitchin fibres over the elliptic locus. We show that orbifold singularities appear in the $\text{PGL}_n$-moduli space $M^{ell}(\text{PGL}_n)$ exactly when the $\text{SL}_n$ side…
It has been argued recently that mirror symmetry exchanges two pure spinors characterizing a generic manifold with SU(3)-structure. We show how pure spinors are modified in the presence of topological D-branes, so that they are still…
We give an introduction to mirror symmetry of strings on Calabi-Yau manifolds with an emphasis on its applications e.g. for the computation of Yukawa couplings. We introduce all necessary concepts and tools such as the basics of toric…
New geometrical features of the Landau-Ginzburg orbifolds are presented, for models with a typical type of superpotential. We show the one-to-one correspondence between some of the $(a,c)$ states with $U(1)$ charges $(-1,1)$ and the…
We prove one direction of homological mirror symmetry for complete intersections in algebraic tori, in all dimensions. The mirror geometry is not a space but a LG model, i.e. a pair given by a space and a regular function. We show that the…
Given a non-singular variety with a K3 fibration f : X --> S we construct dual fibrations Y --> S by replacing each fibre X_s of f by a two-dimensional moduli space of stable sheaves on X_s. In certain cases we prove that the resulting…
By applying mirror symmetry to D-branes in a Calabi-Yau geometry we shed light on a $G_2$ flop in M-theory relevant for large $N$ dualities in ${\cal N}=1$ supersymmetric gauge theories. Furthermore, we derive superpotential for M-theory on…
The eigenmirror problem asks: ``When does the reflection of a surface in a curved mirror appear undistorted to an observer?'' We call such a surface an {\em eigensurface} and the corresponding mirror an {\em eigenmirror}. The data for an…
We explain how to relate the problem of finding a mirror manifold for a Calabi-Yau manifold to the problem of characterizing the rational homotopy types of closed K\"{a}hler manifolds.
The purpose of this paper is to exhibit a natural construction between complex geometry and symplectic geometry following the idea of mirror symmetry. Suppose we are given a family of pairs of 2-dimensional K\"ahler tori and stable…
In this paper, we apply the idea of T-duality to projective spaces. From a connection on a line bundle on $\mathbb P^n$, a Lagrangian in the mirror Landau-Ginzburg model is constructed. Under this correspondence, the full strong exceptional…
We define the notion of mirror of a Calabi-Yau manifold with a stable bundle in the context of type II strings in terms of supersymmetric cycles on the mirror. This allows us to relate the variation of Hodge structure for cohomologies…
Mirror symmetry of Calabi-Yau manifolds can be understood via a Legendre duality between a pair of certain affine manifolds with singularities called tropical manifolds. In this article, we study conifold transitions from the point of view…
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 use spectral invariants in Lagrangian Floer theory in order to show that there exist \emph{isometric} embeddings of normed linear spaces (finite or infinite dimensional, depending on the case) into the space of Hamiltonian deformations…
In this short note we prove that in the case of elliptic curves, the isomorphism of generalized complex structure between $T$-dual manifolds described by Cavalcanti-Gualtieri coincides with the mirror map for elliptic curves described by…
We prove homological mirror symmetry for Milnor fibers of simple singularities in dimensions greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv:1806.04345. The proof is based on a relation between matrix…
We give some examples of isomorphisms of moduli of sheaves induced by Fourier-Mukai functor. As applications, we give another proof on deformation type of some moduli spaces of sheaves on abelian and K3 surfaces.