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arXiv · 2506.08385

Maximal minors of $1$-generic matrices have rational singularities

Trung Chau·Manoj Kummini
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Abstract

We show that the quotient ring by the ideal of maximal minors of a $1$-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.

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Trung Chau, Manoj Kummini. 2025-06-10. Maximal minors of $1$-generic matrices have rational singularities. https://arxiv.org/abs/2506.08385

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