Floer cohomology and pencils of quadrics

Abstract

There is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces. We investigate symplectic aspects of this relationship, with a view to applications in low-dimensional topology. We construct a derived equivalence between the Fukaya category of a curve and the nilpotent summand of the Fukaya category of the associated complete intersection of two quadrics. This essentially determines the instanton Floer homology of a 3-manifold fibred by genus two curves.

70 pages, 7 figures. Version 2: corrections and simplifications to the finite determinacy and blowing up arguments; general re-organisation and some auxiliary material removed to appear elsewhere. Version 3: choice of symplectic forms clarified, various typoes corrected

References in corpus (13)

• Functors and Computations in Floer homology with Applications Part II
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Quantum Structures for Lagrangian Submanifolds
• Quilted Floer Cohomology
• Homological Mirror Symmetry for manifolds of general type
• Suspending Lefschetz fibrations, with an application to Local Mirror Symmetry
• Kuranishi homology and Kuranishi cohomology
• A symplectic Gysin sequence
• Toric degeneration and non-displaceable Lagrangian tori in $S^2\times S^2$
• Gluing pseudoholomorphic quilted disks
• Homological mirror symmetry for curves of higher genus
• Compactness for holomorphic curves with switching Lagrangian boundary conditions

Cited by in corpus (1)

• Poisson brackets and symplectic invariants