Maximal minors of $1$-generic matrices have rational singularities
Commutative Algebra
2025-06-11 v1 Algebraic Geometry
Abstract
We show that the quotient ring by the ideal of maximal minors of a -generic matrix has rational singularities. This answers a conjecture of Eisenbud (1988) that such rings are normal, and generalizes a result of Conca, Mostafazadehfard, Singh and Varbaro (2018) that generic Hankel determinantal rings have rational singularities in characteristic zero.
Keywords
Cite
@article{arxiv.2506.08385,
title = {Maximal minors of $1$-generic matrices have rational singularities},
author = {Trung Chau and Manoj Kummini},
journal= {arXiv preprint arXiv:2506.08385},
year = {2025}
}
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