Journal of Symplectic Geometry

Volume 17 (2019)

Number 5

Twin Lagrangian fibrations in mirror symmetry

Pages: 1331 – 1387



Naichung Conan Leung (Institute of Mathematical Sciences and Department of Mathematics, Chinese University of Hong Kong)

Yin Li (King’s College London, United Kingdom)


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.

Received 11 November 2015

Accepted 5 September 2018

Published 20 November 2019