Components and singularities of Quot schemes and varieties of commuting matrices

@article{Jelisiejew2022ComponentsAS,
title={Components and singularities of Quot schemes and varieties of commuting matrices},
author={Joachim Jelisiejew and Klemen {\vS}ivic},
journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
year={2022},
volume={2022},
pages={129 - 187}
}
• Published 24 June 2021
• Mathematics
• Journal für die reine und angewandte Mathematik (Crelles Journal)
Abstract We investigate the variety of commuting matrices. We classify its components for any number of matrices of size at most 7. We prove that starting from quadruples of 8×8{8\times 8} matrices, this scheme has generically nonreduced components, while up to degree 7 it is generically reduced. Our approach is to recast the problem as deformations of modules and generalize an array of methods: apolarity, duality and Białynicki–Birula decompositions to this setup. We include a thorough review…
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