Versality in mirror symmetry
arXiv:1804.00616 · doi:10.4310/CDM.2017.v2017.n1.a2
Abstract
One of the attractions of homological mirror symmetry is that it not only implies the previous predictions of mirror symmetry (e.g., curve counts on the quintic), but it should in some sense be `less of a coincidence' than they are and therefore easier to prove. In this survey we explain how Seidel's approach to mirror symmetry via versality at the large volume/large complex structure limit makes this idea precise.
arXiv comment43 pages, 4 figures. Survey for the proceedings of the conference Current Developments in Mathematics 2017
References in corpus (31)
- Deformation quantization of Poisson manifolds, I
- Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
- Functors and Computations in Floer homology with Applications Part II
- Mirror symmetry, Langlands duality, and the Hitchin system
- Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
- Equivariant Gromov - Witten Invariants
- Cyclic symmetry and adic convergence in LagrangianFloer theory
- Homological Mirror Symmetry for Calabi-Yau hypersurfaces in projective space
- Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties
- Symplectic cohomology and duality for the wrapped Fukaya category
- Fukaya categories and deformations
- Deformation theory via differential graded Lie algebras
- Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I
- Homological Mirror Symmetry for manifolds of general type
- The Monomial-Divisor Mirror Map
- Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors
- Arboreal Singularities
- Mirror symmetry: from categories to curve counts
- Mirror symmetry for very affine hypersurfaces
- Non-characteristic expansions of Legendrian singularities
- An algebraic proof of Bogomolov-Tian-Todorov theorem
- A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
- Lectures on Mirror Symmetry, Derived Categories, and D-branes
- Homological mirror symmetry for the four-torus
- Topological Fukaya category and mirror symmetry for punctured surfaces
- Symmetries of Lagrangian fibrations
- Cyclic homology, -equivariant Floer cohomology, and Calabi-Yau structures
- Generators in formal deformations of categories
- Computing a categorical Gromov-Witten invariant
- Higher algebraic structures in Hamiltonian Floer theory I
- Automatic split-generation for the Fukaya category