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arXiv · 2112.04844

The $a_0$-invariants of powers of a two-dimensional squarefree monomial ideal

Lizhong Chu·Dancheng Lu
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Abstract

Let $\Delta$ be an one-dimensional simplicial complex on $\{1,2,\ldots,s\}$ and $S$ the polynomial ring $K[x_1,\ldots,x_s]$ over a field $K$. The explicit formula for $a_0(S/I_{\Delta}^n)$ is presented when $\mathrm{girth}(\Delta)\geq 4$. If $\mathrm{girth}(\Delta)=3$ we characterize the simplicial complexes $\Delta$ for which $a_0(S/I_{\Delta}^n)=3n-1$ or $3n-2$.

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Lizhong Chu, Dancheng Lu. 2021-12-09. The $a_0$-invariants of powers of a two-dimensional squarefree monomial ideal. https://arxiv.org/abs/2112.04844

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