INVARIANT HILBERT SCHEME OF THE COX REALIZATION OF THE NILPOTENT CONE IN $¥mathfrak{sl}$($n$) (Women in Mathematics)

Abstract

The invariant Hilbert scheme is a moduli space of schemes which aer stable under an action of a reductive algebraic group. By a suitable choice of the parameter, it becomes a candidate for a resolution of singularities of a quotient singularity. In this short talk, I will explain two main problems in the study of the invariant Hilbert scheme from the point of view of birational geometry of singularities.