Hoai Dao, Oklahoma State University
Authors: Hoai Dao
2022 AWM Research Symposium
Poster Presentation

Let $k$ be a field, $S=k[x_{1},\dots, x_{n}]$ a polynomial ring and $\mathbf{m}=(x_{1},\dots, x_{n}$ the maximal ideal. Let $I=\mathbf{m}^{d}$ for some $d$. Then $I$ is a Borel ideal which is generated by all monomials of degree $d$, say $m_{1},\dots, m_{s}$. Let $\widehat{I}_{I}=(m_{1},\dots, \widehat{m_{I}},\dots, m_{s})$. Observe that if $m_{i}=x_{j}^{d}$ for some $j$, then $S/\widehat{I_{I}}$ is minimally resolved by the Eliahou-Kervaire resolution. Our goal is to describe the minimal resolutions of all $\widehat{I_{I}}$.

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