Homological mirror symmetry for the quartic surface

Abstract

This proves Kontsevich's mirror conjecture for (on the symplectic side) a quartic surface in P^3.

v2: Revision changes one step in the proof, and makes minor expository changes elsewhere; v3: small expository changes as suggested by referees; v4: typo removal

References in corpus (4)

• Fukaya categories and deformations
• D-branes on Calabi-Yau Manifolds and Superpotentials
• Amoebas of algebraic varieties
• Convergence of Hermitian-Yang-Mills Connections on Kähler Surfaces and mirror symmetry

Cited by in corpus (38)

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• Fukaya categories of the torus and Dehn surgery
• Matrix Factorizations and Representations of Quivers I
• Mirror symmetry for very affine hypersurfaces
• Global topology of the Hitchin system
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• Topological conformal field theories and Calabi-Yau categories
• Curved A-infinity algebras and Landau-Ginzburg models
• Stability conditions on $A_n$-singularities
• Homological mirror symmetry for $A_n$-resolutions as a $T$-duality
• Period- and mirror-maps for the quartic K3
• Ribbon Graphs and Mirror Symmetry I
• Compact moduli of noncommutative projective planes
• Sheaves on local Calabi-Yau varieties
• Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}
• Slow entropy and symplectomorphisms of cotangent bundles
• Automorphisms and autoequivalences of generic analytic K3 surfaces
• Floer homology of Lagrangian submanifolds
• Homological mirror symmetry for punctured spheres
• Mirror symmetry for Berglund-Hübsch Milnor fibers
• K3 mirror symmetry, Legendre family and Deligne's conjecture for Fermat quartic
• Finite group actions on Lagrangian Floer theory
• Homological mirror symmetry of Fermat polynomials
• Equivariant split generation and mirror symmetry of special isogenous tori
• Polytopes and Skeleta
• Homological mirror symmetry and Fourier-Mukai transform
• The Picard-Lefschetz theory of complexified Morse functions
• Complex K-theory of mirror pairs
• On the counting of holomorphic discs in toric Fano manifolds
• Mirror Symmetry in dimension one and Fourier-Mukai equivalences
• DG quivers of smooth rational surfaces
• On the Fukaya Categories of Higher Genus Surfaces
• Time and a Temporally Statistical Quantum Geometrodynamics
• Seidel's Mirror Map for the Torus
• D-branes and synthetic/$C^{\infty }$-algebraic symplectic/calibrated geometry, I: Lemma on a finite algebraicness property of smooth maps from Azumaya/matrix manifolds
• Homological Mirror Symmetry for Toric del Pezzo Surfaces
• Generalized Calabi-Yau structures, K3 surfaces, and B-fields
• D-particle Field Category