The variety of pairs of commuting nilpotent matrices is irreducible

@article{Baranovsky2001TheVO,
  title={The variety of pairs of commuting nilpotent matrices is irreducible},
  author={V. Baranovsky},
  journal={Transformation Groups},
  year={2001},
  volume={6},
  pages={3-8}
}
In this paper we prove the dimension and the irreduciblity of the variety parametrizing all pairs of commuting nilpotent matrices. Our proof uses the connection between this variety and the punctual Hilbert scheme of a smooth algebraic surface. 
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