Abstract
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 P 2 in the sense of Kashiwara.
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