Hessenberg variety

A Hessenberg variety is a type of algebraic variety that arises in the context of representations of Lie algebras and algebraic geometry. Specifically, Hessenberg varieties are associated with a choice of a nilpotent operator on a vector space and a subspace that captures certain "Hessenberg" conditions. They can be thought of as a geometric way to study certain types of matrices or linear transformations up to a specified degree of nilpotency.