# Hilbert schemes on plane curve singularities are generalized affine Springer fibers

@inproceedings{Garner2020HilbertSO, title={Hilbert schemes on plane curve singularities are generalized affine Springer fibers}, author={Niklas Garner and Oscar Kivinen}, year={2020} }

In this paper, we show that Hilbert schemes of planar curve singularities can be interpreted as generalized affine Springer fibers for $GL_n$. This leads to a construction of a rational Cherednik algebra action on their homology, which we compute in examples. This work was inspired in part by a construction in three-dimensional $\mathcal{N}=4$ gauge theory.

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