Acta Mathematica Vietnamica
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Mixed Commuting Varieties over Nilpotent Matrices
Jerry Magana
,
Nham V. Ngo
Abstract
We give an explicit description of all irreducible components and their dimensions of mixed commuting varieties over nilpotent 3 × 3 matrices, hence describing the varieties of 3-dimensional modules for certain quotients of polynomial algebras over an algebraically closed field. Our results also provide insights on support varieties of simple modules over Frobenius kernels of $SL_3$.