Hodge structure

A Hodge structure is a concept in algebraic geometry and differential geometry that is used to study the relationships between algebraic and topological properties of complex manifolds. It provides a bridge between the geometric structure of a manifold and its algebraic properties. A Hodge structure on a vector space \( V \) over the complex numbers can be described as a decomposition of the space into subspaces that reflect the complex geometry of the underlying manifold.