论文标题
Ishida综合体的概括与应用
A Generalization of the Ishida Complex with applications
论文作者
论文摘要
我们构建了一个普遍的ISHIDA复合物，以通过细胞二项式理想对多项式环对多项式环对多项式环的商的单一支持进行计算。结果，我们获得了一个组合标准，以确定何时cohen-macaulay。特别是，这给出了针对晶格理想的cohen--macaulayness标准。我们还证明了将局部同胞学与仿期半群环与局部同胞的根治性的理想支持有关的结果，并通过自由基单体理想对仿期半群环的商的最大理想支持。这需要对半群的组合假设，该假设适用于（不一定是正常的）半群，其锥形是单纯形的锥体。
We construct a generalize Ishida complex to compute the local cohomology with monomial support of modules over quotients of polynomial rings by cellular binomial ideals. As a consequence, we obtain a combinatorial criterion to determine when such a quotient is Cohen--Macaulay. In particular, this gives a Cohen--Macaulayness criterion for lattice ideals. We also prove a result relating the local cohomology with radical monomial ideal support of an affine semigroup ring to the local cohomology with maximal ideal support of the quotient of the affine semigroup ring by the radical monomial ideal. This requires a combinatorial assumption on the semigroup, which holds for (not necessarily normal) semigroups whose cone is the cone over a simplex.
