New example of modified moduli space of special Bohr - Sommerfeld lagrangian submanifolds

TL;DR

This paper provides a specific example of a modified moduli space for special Bohr-Sommerfeld Lagrangian submanifolds, focusing on the full flag variety of ^3 in ^3 with a particular bundle.

Contribution

It introduces a new example of the modified moduli space in the context of algebraic geometry and symplectic topology, specifically for the full flag variety and a half-canonical bundle.

Findings

Explicit construction of the modified moduli space for the given variety.

Identification of properties of special Bohr-Sommerfeld Lagrangian submanifolds in this setting.

Insights into the geometric structure of the moduli space.

Abstract

We present an example of modified moduli space of special Bohr - Sommerfeld lagrangian submanifolds for the case when the given algebraic variety is the full flag $F^3$ for $\mathbb{C}^3$ and the very ample bundle is $K^{- \frac{1}{2}}_{F^3}$