Transformation Groups

, Volume 6, Issue 1, pp 3–8 | Cite as

The variety of pairs of commuting nilpotent matrices is irreducible

  • V. Baranovsky


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.


Topological Group Algebraic Surface Hilbert Scheme Nilpotent Matrice Punctual Hilbert Scheme 
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© Birkhäuser 2001

Authors and Affiliations

  • V. Baranovsky
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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