The Moduli Space of D-Exact Lagrangian Submanifolds
This paper studies the Lagrangian geometry of algebraic varieties. Given a smooth compact
simply-connected algebraic variety, we construct a family of finite-dimensional K¨ahler manifolds
whose elements are the equivalence classes of Lagrangian submanifolds satisfying our new D-exactness
condition. In connection with the theory of Weinstein structures, these moduli spaces turn out related
to the special Bohr–Sommerfeld geometry constructed by the author previously. This enables us to
extract from the moduli spaces some stable components and conjecture that they are not only K¨ahler but also algebraic.