Some schemes related to the commuting variety

Author:
Allen Knutson

Journal:
J. Algebraic Geom. **14** (2005), 283-294

DOI:
https://doi.org/10.1090/S1056-3911-04-00389-3

Published electronically:
October 26, 2004

MathSciNet review:
2123231

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Abstract | References | Additional Information

Abstract: The *commuting variety* is the pairs of matrices such that . We introduce the **diagonal commutator scheme**, is diagonal, which we prove to be a reduced complete intersection, one component of which is the commuting variety. (We conjecture there to be only one other component.)

The diagonal commutator scheme has a flat degeneration to the scheme lower triangular, upper triangular, which is again a reduced complete intersection, this time with components (one for each permutation). The degrees of these components give interesting invariants of permutations.

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Additional Information

**Allen Knutson**

Affiliation:
Department of Mathematics, University of California, Berkeley, 1033 Evans Hall, Berkeley, California 94720-3840

Email:
allenk@math.berkeley.edu

DOI:
https://doi.org/10.1090/S1056-3911-04-00389-3

Received by editor(s):
June 23, 2003

Published electronically:
October 26, 2004

Additional Notes:
The author was supported by the National Science Foundation and the Sloan Foundation.