Special Bohr - Sommerfeld lagrangian submanifolds in algebraic varieties

TL;DR

This paper introduces a new concept of speciality for Bohr-Sommerfeld Lagrangian submanifolds in algebraic varieties, leading to the construction of finite-dimensional moduli spaces applicable in geometric quantization and mirror symmetry.

Contribution

It defines a novel notion of speciality for Bohr-Sommerfeld Lagrangian submanifolds and constructs associated algebraic moduli spaces from ample line bundles.

Findings

Constructs finite-dimensional algebraic moduli spaces

Applicable in geometric quantization and mirror symmetry

Provides a new framework for studying Lagrangian submanifolds

Abstract

We present a new notion of speciality which is valid for Bohr - Sommerfeld lagrangian submanifolds. For algebraic varieties it leads to the construction of finite dimensional moduli spaces which are algebraic starting with any ample line bundle. The construction can be exploited both in Geometric Quantization and Mirror Symmetry.