Seshadri theorem

Seshadri's theorem concerns the relationship between vector bundles and group actions on algebraic varieties. It states that a vector bundle on a projective variety is semi-stable if and only if it can be realized as the quotient of a trivial bundle by a group action that is compatible with the bundle’s structure. In simpler terms, it links the geometric concept of "semi-stability" of certain mathematical objects to the ability to describe them as symmetric, well-behaved quotients under group symmetries, providing a bridge between geometric stability and symmetry-based constructions.