(The) topology of hessenberg varieties

Abstract

In 1988, De Mari introduced the Hessenberg variety of degree p which is the subvariety of a complete flag manifold and showed the algebraic conditions determining the Hessenberg variety of degree p and the connectedness of the Hessenberg variety of degree p. The Hessenberg variety of degree p is the Hessenberg variety associated with a Hessenberg function h such that $h(i) = i + p if i + p \leq n and h(i) = n if i+p > n$. n this thesis, we show the algebraic conditions determining the Hessenberg variety of a general Hessenberg function and the connectedness of the hessenberg variety of a general Hessenberg function. Furthermore, we introduce the equivariant cohomology rings of regular nilpotent hessenberg varieties in Lie tpye A which is the recent result of [2].