论文标题
hodge hodge hyperface的理想
Hodge ideals for the determinant hypersurface
论文作者
论文摘要
我们明确确定决定性超表面的hodge理想是确定性理想的符号能力的相交。我们通过研究n x n矩阵空间x上的常规函数的混合霍奇模块O_x（*z）上的hodge和重量过滤来证明我们的结果，并在奇异矩阵的除数Z沿极点。 O_x（*Z）上的重量过滤的组成因子是纯hodge模块，其基本的D模块由X上简单的GL-等分D-Modules给出，其中GL是自然的对称性组，由矩阵条目上的行和列操作作用。通过利用其相关分级的GL-均衡性和Cohen-Macaulay特性，我们在简单的GL-量相位D模块上明确描述了可能的Hodge过滤，这是由相应权重确定的唯一偏移。对于非平方矩阵，O_X（*Z）自然被局部的同胞模块H^J_z（X，O_X）代替，后者原来是纯Hodge模块。通过明确处理确定性品种奇异性的一些自然分析定理，并在方形矩阵上使用结果，我们确定了这些局部共同体模块的权重和Hodge过滤。
We determine explicitly the Hodge ideals for the determinant hypersurface as an intersection of symbolic powers of determinantal ideals. We prove our results by studying the Hodge and weight filtrations on the mixed Hodge module O_X(*Z) of regular functions on the space X of n x n matrices, with poles along the divisor Z of singular matrices. The composition factors for the weight filtration on O_X(*Z) are pure Hodge modules with underlying D-modules given by the simple GL-equivariant D-modules on X, where GL is the natural group of symmetries, acting by row and column operations on the matrix entries. By taking advantage of the GL-equivariance and the Cohen-Macaulay property of their associated graded, we describe explicitly the possible Hodge filtrations on a simple GL-equivariant D-module, which are unique up to a shift determined by the corresponding weights. For non-square matrices, O_X(*Z) is naturally replaced by the local cohomology modules H^j_Z(X,O_X), which turn out to be pure Hodge modules. By working out explicitly the Decomposition Theorem for some natural resolutions of singularities of determinantal varieties, and using the results on square matrices, we determine the weights and the Hodge filtration for these local cohomology modules.
