The ADHM Variety and Perverse Coherent Sheaves

Abstract

We study the full set of solutions to the ADHM equation as an affine algebraic set, the ADHM variety. We gather the points 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 connect representations of the ADHM quiver to coherent perverse sheaves on ${\mathbb{P}}^2$ in the sense of Kashiwara.

19 pages.

References in corpus (2)

• Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
• Moduli spaces of framed perverse instantons on P^3

Cited by in corpus (4)

• ADHM construction of perverse instanton sheaves
• Commuting matrices and the Hilbert scheme of points on affine spaces
• Moduli spaces of framed flags of sheaves on the projective plane
• Holomorphic pre-symplectic form on the nested Hilbert scheme $\mbox{Hilb}^{3,4}(\mathbb{C}^2)$