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<p>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 (Amer J Math 110(3):541–575, 1988) that such rings are normal, and generalizes a result of Conca et al. (Adv Math 335:111–129, 2018) that generic Hankel determinantal rings have rational singularities in characteristic zero.</p>

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Maximal minors of 1-generic matrices have rational singularities

  • 期刊论文

  • 发表日期：

    2025年11月26日

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  • Trung Chau,
  • Manoj Kummini

摘要

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 (Amer J Math 110(3):541–575, 1988) that such rings are normal, and generalizes a result of Conca et al. (Adv Math 335:111–129, 2018) that generic Hankel determinantal rings have rational singularities in characteristic zero.