Blowup Algebras of $n$--dimensional Ferrers Diagrams

Kuei-Nuan Lin; Yi-Huang Shen

Blowup Algebras of $n$--dimensional Ferrers Diagrams

Commutative Algebra 2025-02-05 v1 Combinatorics

Authors: Kuei-Nuan Lin , Yi-Huang Shen

Abstract

We demonstrate that the direct sum of ideals satisfying the strong $\ell$ -exchange property is of fiber type. Furthermore, we provide Gr\"obner 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.

Keywords

blowup algebras Ferrers diagrams multi-Rees algebras Gröbner bases Koszul algebras Cohen–Macaulay rings fiber type ideals

Cite

@article{arxiv.2502.01917,
  title  = {Blowup Algebras of $n$--dimensional Ferrers Diagrams},
  author = {Kuei-Nuan Lin and Yi-Huang Shen},
  journal= {arXiv preprint arXiv:2502.01917},
  year   = {2025}
}

Comments

12 pages, 1 figure, to appear in Proceedings of the American Mathematical Society

Blowup Algebras of $n$--dimensional Ferrers Diagrams

Abstract

Keywords

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