Related papers: Noncommutative homological mirror functor
This paper gives a new way of constructing Landau-Ginzburg mirrors using deformation theory of Lagrangian immersions motivated by the works of Seidel, Strominger-Yau-Zaslow and Fukaya-Oh-Ohta-Ono. Moreover we construct a canonical functor…
We prove an equivalence of two A-infinity functors, via Orlov's Landau-Ginzburg/Calabi-Yau correspondence. One is the Polishchuk-Zaslow's mirror symmetry functor of elliptic curves, and the other is a localized mirror functor from the…
Given a Lagrangian fibration, we provide a natural construction of a mirror Landau-Ginzburg model consisting of a rigid analytic space, a superpotential function, and a dual fibration based on Fukaya's family Floer theory. The mirror in the…
We develop a method of gluing the local mirrors and functors constructed from immersed Lagrangians in the same deformation class. As a result, we obtain a global mirror geometry and a canonical mirror functor. We apply the method to…
We find a relation between Lagrangian Floer pairing of a symplectic manifold and Kapustin-Li pairing of the mirror Landau-Ginzburg model under localized mirror functor. They are conformally equivalent with an interesting conformal factor…
Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X, we define a holomorphic function W known as the Floer potential. We construct a canonical A-infinity functor from the Fukaya category of X to the category of matrix…
A categorical formalism is introduced for studying various features of the symplectic geometry of Lefschetz fibrations and the algebraic geometry of Tyurin degenerations. This approach is informed by homological mirror symmetry, derived…
We prove a homological mirror symmetry result for maximally degenerating families of hypersurfaces in $(\mathbb{C}^*)^n$ (B-model) and their mirror toric Landau-Ginzburg A-models. The main technical ingredient of our construction is a…
In mirror symmetry, symplectic Landau-Ginzburg models are mirror to a large class of examples, in particular to Fano varieties and hypersurfaces of many Calabi-Yau and Fano varieties. When studying their Fukaya categories on the A-model in…
Mirror symmetry for higher genus curves is usually formulated and studied in terms of Landau-Ginzburg models; however the critical locus of the superpotential is arguably of greater intrinsic relevance to mirror symmetry than the whole…
We show homological mirror symmetry results relating coherent analytic sheaves on some complex elliptic surfaces and objects of certain Fukaya categories. We first define the notion of a non-algebraic Landau-Ginzburg model on $\mathbb{R}…
We interpret symplectic geometry as certain sheaf theory by constructing a sheaf of curved A_\infty algebras which in some sense plays the role of a "structure sheaf" for symplectic manifolds. An interesting feature of this "structure…
We prove that the Landau--Ginzburg superpotential of del Pezzo surfaces can be realized as a limit of their hyperK\"ahler rotation toward the large complex structure limit point. As a corollary, we compute the limit of the complex affine…
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…
For each sphere with three orbifold points, we construct an algorithm to compute the open Gromov-Witten potential, which serves as the quantum-corrected Landau-Ginzburg mirror and is an infinite series in general. This gives the first class…
We construct a family of Lagrangian submanifolds in the Landau--Ginzburg mirror to the projective plane equipped with a binodal cubic curve as anticanonical divisor. These objects correspond under mirror symmetry to the powers of the…
Polishchuk-Zaslow explained the homological mirror symmetry between Fukaya category of symplectic torus and the derived category of coherent sheaves of elliptic curves via Lagrangian torus fibration. Recently, Cho-Hong-Lau found another…
We introduce a duality of Landau-Ginzburg models based on the notion of the discrete Legendre transform given by Gross-Siebert. It generalizes the duality used to construct mirrors of complete intersections in toric varieties in a recent…
Let M be a Weinstein four-manifold mirror to Y\D for (Y,D) a log Calabi--Yau surface; intuitively, this is typically the Milnor fibre of a smoothing of a cusp singularity. We introduce two families of symplectomorphisms of M: Lagrangian…
For a del Pezzo surface of degree $\geq 3$, we compute the oscillatory integral for its mirror Landau-Ginzburg model in the sense of Gross-Hacking-Keel [Mark Gross, Paul Hacking, and Sean Keel, "Mirror symmetry for log Calabi-Yau surfaces…