The ADHM variety and perverse coherent sheaves

We study the full set of solutions to the ADHM equation as an affine algebraic set, the ADHM variety. We determine a filtration of the ADHM variety into subvarieties according to the dimension of the stabilizing subspace. We compute dimension, and analyze singularity and reducibility of all of these varieties. We also establish a connection between arbitrary solutions of the ADHM equation and coherent perverse sheaves on P2P2 in the sense of Kashiwara.

► We study a stratification of the full set of solutions of the ADHM equation. ► We compute dimension, and analyze singularity and reducibility of all strata. ► Points in each strata are viewed as perverse coherent sheaves on the projective plane.