The degeneration order of simultaneous similarity classes of 3×3 nilpotent matrix tuples is given by rank conditions.
Kirwan,Cohomology of Quotients in Symplectic and Algebraic Geometry, Mathematical Notes 31, Princeton University Press, Princeton, NJ, 1984
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Degeneration order of $3\times 3$ nilpotent matrix tuples
The degeneration order of simultaneous similarity classes of 3×3 nilpotent matrix tuples is given by rank conditions.