Blowup algebras of 𝑛-dimensional Ferrers diagrams

Lin, Kuei-Nuan; Shen, Yi-Huang

doi:10.1090/proc/17249

Blowup algebras of $n$-dimensional Ferrers diagrams
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by Kuei-Nuan Lin and Yi-Huang Shen;

Proc. Amer. Math. Soc. 153 (2025), 2269-2282

DOI: https://doi.org/10.1090/proc/17249

Published electronically: April 8, 2025

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Abstract:

We demonstrate that the direct sum of ideals satisfying the strong $\ell$-exchange property is of fiber type. Furthermore, we provide Gröbner bases of the presentation ideals of multi-Rees algebras and the corresponding special fibers, when they are associated with an $n$-dimensional Ferrers diagram that is standardizable. In particular, we show that these blowup algebras are Koszul Cohen–Macaulay normal domains and classify their singularities.

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Proceedings of the American Mathematical Society

Blowup algebras of $n$-dimensional Ferrers diagrams
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Abstract: