多重分次的特殊化与格理想的算术秩
Specializations of multigradings and the arithmetical rank of lattice ideals
摘要：
在这篇文章中，我们研究了多重分次的特殊化，并将其应用于计算格理想$I_{L_{\mathcal{G}}} \subset K[x_{1},...,x_{n}]$的算术秩的问题。对于$\mathcal{G}$的适当专门化$\mathcal{F}$，$I_{L_{\mathcal{G}}}$的算术秩等于$I_{L_{\mathcal{G}}}$的$\mathcal{F}$ -齐次算术秩。对于格理想$I_{L_{\mathcal{G}}}$和$\mathcal{G}$的每个特化$\mathcal{F}$，我们关联一个单纯复形。我们证明了单纯复形的组合不变量提供了$I_{L_{\mathcal{G}}}$的$\mathcal{F}$ -齐次算术秩的下界。
英文摘要：
In this article we study specializations of multigradings and apply them to the problem of the computation of the arithmetical rank of a lattice ideal $I_{L_{\mathcal{G}}} \subset K[x_{1},...,x_{n}]$. The arithmetical rank of $I_{L_{\mathcal{G}}}$ equals the $\mathcal{F}$-homogeneous arithmetical rank of $I_{L_{\mathcal{G}}}$, for an appropriate specialization $\mathcal{F}$ of $\mathcal{G}$. To the lattice ideal $I_{L_{\mathcal{G}}}$ and every specialization $\mathcal{F}$ of $\mathcal{G}$ we associate a simplicial complex. We prove that combinatorial invariants of the simplicial complex provide lower bounds for the $\mathcal{F}$-homogeneous arithmetical rank of $I_{L_{\mathcal{G}}}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
