Corpus ID: 216868242

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. 
1 Citations
Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra
In this note we explicitly construct an action of the rational Cherednik algebra $H_{1,m/n}(S_n,\mathbb{C}^n)$ corresponding to the permutation representation of $S_n$ on theExpand

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