Lagrangian Floer theory on compact toric manifolds II: bulk deformations
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In this paper, the authors used the deformations of Lagrangian cohomology by the ambient cycles, which they call bulk deformations, to find a continuum of non-displaceable fibers on some compact toric manifolds.Abstract:
This is a continuation of part I in the series of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian fibers on some compact toric manifolds. We also provide a method of finding all fibers with non-vanishing Floer cohomology with bulk deformations in arbitrary compact toric manifolds, which we call bulk-balanced Lagrangian fibers.read more
Citations
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Homological Mirror Symmetry for the genus two curve
TL;DR: In this paper, the Fukaya category of a genus two curve was shown to be equivalent to the category of Landau-Ginzburg branes on a singular rational surface.
Journal ArticleDOI
Cyclic symmetry and adic convergence in LagrangianFloer theory
TL;DR: In this paper, the authors used continuous family of multisections of the moduli space of pseudo holomorphic discs to partially improve, in the case of real coefficient, the construction of Lagrangian Floer cohomology of which the author developed jointly with Oh-Ohta Ono.
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Homological mirror symmetry for the genus two curve
Abstract: Katzarkov has proposed a generalization of Kontsevich's mirror symmetry conjecture, covering some varieties of general type. We prove a version of this conjecture in the simplest example, relating the Fukaya category of a genus two curve to the category of Landau-Ginzburg branes on a certain singular rational surface.
Journal ArticleDOI
Mirror symmetry for P^2 and tropical geometry
TL;DR: The relationship between mirror symmetry for P 2, at the level of big quantum cohomology, and tropical geometry was explored in this article, where it was shown that mirror symmetry is equivalent in a strong sense to tropical curve counting formulas, including tropical formulas for gravitational descendent invariants.
Journal ArticleDOI
On the Fukaya category of a Fano hypersurface in projective space
TL;DR: In this paper, the main structures of the Fukaya category of a Fano hypersurface were established in the monotone case: the closed-open string maps, weak proper Calabi-Yau structure, Abouzaid's split-generation criterion, and their analogues when weak bounding cochains are included.
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