论文标题
晶格理想的最小分辨率
Minimal resolutions of lattice ideals
论文作者
论文摘要
在多项式环上，任意辅助艺术晶格理想的规范最小的自由分辨率均在任何特征为0或任何有限的积极素数的场上构建。差速器具有封闭形式的组合描述，作为$ \ mathbb {z}^n $的晶格路径的总和，这些权重来自由晶格点索引的简单复合物中的面部序列。在任何特征的领域，通过选择沿晶格路径跨越树的高维类似物的选择来构建非典型但更简单的分辨率。这些构造通过将它们等效于晶格模块来推广Sylvan的单一理想分辨率。
A canonical minimal free resolution of an arbitrary co-artinian lattice ideal over the polynomial ring is constructed over any field whose characteristic is 0 or any but finitely many positive primes. The differential has a closed-form combinatorial description as a sum over lattice paths in $\mathbb{Z}^n$ of weights that come from sequences of faces in simplicial complexes indexed by lattice points. Over a field of any characteristic, a non-canonical but simpler resolution is constructed by selecting choices of higher-dimensional analogues of spanning trees along lattice paths. These constructions generalize sylvan resolutions for monomial ideals by lifting them equivariantly to lattice modules.
