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. 
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References

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Homology of Hilbert schemes of points on a locally planar curve
Global Springer theory
Hecke correspondences for Hilbert schemes of reducible locally planar curves
Affine Springer fibers of type A and combinatorics of diagonal coinvariants
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Macdonald formula for curves with planar singularities
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