An algebro-geometric realization of the cohomology ring of Hilbert scheme of points in the affine plane

2015/01/11 by Hikita, Tatsuyuki · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1501.02430

Abstract

We show that the cohomology ring of Hilbert scheme of n-points in the affine plane is isomorphic to the coordinate ring of \mathbbG_m-fixed point scheme of the n-th symmetric product of ℂ² for a natural \mathbbG_m-action on it. This result can be seen as an analogue of a theorem of DeConcini, Procesi and Tanisaki on a description of the cohomology ring of Springer fiber of type A.

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• Minimal Nilpotent Orbits and Toric Varieties
• Slant sums of quiver gauge theories

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