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arXiv · 1501.02430

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

Tatsuyuki Hikita
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Abstract

We show that the cohomology ring of Hilbert scheme of $n$-points in the affine plane is isomorphic to the coordinate ring of $\mathbb{G}_{m}$-fixed point scheme of the $n$-th symmetric product of $\mathbb{C}^{2}$ for a natural $\mathbb{G}_{m}$-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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Tatsuyuki Hikita. 2015-01-11. An algebro-geometric realization of the cohomology ring of Hilbert scheme of points in the affine plane. https://arxiv.org/abs/1501.02430

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