Lagrangian geometry of algebraic varieties

TL;DR

This paper explores the Lagrangian geometry of algebraic varieties by viewing them as symplectic manifolds with Kahler forms, introducing two fundamental constructions applicable to many varieties.

Contribution

It introduces two basic constructions for studying Lagrangian geometry on algebraic varieties, broadening the scope of symplectic and Kahler geometry applications.

Findings

Established foundational constructions for Lagrangian geometry on algebraic varieties

Connected algebraic geometry with symplectic and Kahler geometry frameworks

Provided tools for further exploration of Lagrangian structures in algebraic contexts

Abstract

Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a sufficiently wide set of algebraic varieties.