Twin Lagrangian fibrations in mirror symmetry
arXiv:1506.04625
Abstract
A twin Lagrangian fibration, originally introduced by Yau and the first author, is roughly a geometric structure consisting of two Lagrangian fibrations whose fibers intersect with each other cleanly. In this paper, we show the existence of twin Lagrangian fibrations on certain symplectic manifolds whose mirrors are fibered by rigid analytic cycles. Using family Floer theory in the sense of Fukaya and Abouzaid, these twin Lagrangian fibrations are shown to be induced from fibrations by rigid analytic subvarieties on the mirror. As additional evidences, we discuss two simple applications of our constructions.
35 pages, 2 fiigures; v6: Final version, to appear in Journal of Symplectic Geometry
References in corpus (11)
- Mirror symmetry and T-duality in the complement of an anticanonical divisor
- Quantum Structures for Lagrangian Submanifolds
- Family Floer cohomology and mirror symmetry
- Gauge theory and mirror symmetry
- Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P^1_{a,b,c}
- Semi-global invariants of piecewise smooth Lagrangian fibrations
- Localized mirror functor constructed from a Lagrangian torus
- Finite group actions on Lagrangian Floer theory
- Equivariant split generation and mirror symmetry of special isogenous tori
- Disjoinable Lagrangian tori and semisimple symplectic cohomology
- Twin relationships in Parsimonious Games: some results