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Transformation Groups

, Volume 6, Issue 1, pp 3–8 | Cite as

The variety of pairs of commuting nilpotent matrices is irreducible

  • V. Baranovsky
Article

Abstract

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.

Keywords

Topological Group Algebraic Surface Hilbert Scheme Nilpotent Matrice Punctual Hilbert Scheme 
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Copyright information

© Birkhäuser 2001

Authors and Affiliations

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

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