The ADHM Variety and Perverse Coherent Sheaves

Details The ADHM Variety and Perverse Coherent Sheaves The ADHM Variety and Perverse Coherent Sheaves

2010-05-05

arxiv.org/abs/1005.0807v1

J. Geom. Phys. 61 (2011), 2219-2232

Mathematics

Algebraic Geometry

19 pages.

Scientific paper

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.

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