论文标题
最大未成年人和亚最大Pfaffians的增厚的局部共同体学模块的SOCLE学位
Socle degrees for local cohomology modules of thickenings of maximal minors and sub-maximal Pfaffians
论文作者
论文摘要
令$ s $为非方块通用矩阵或奇数偏斜的矩阵空间的多项式环，让$ i $是最大未成年人或$ \ operatatorname {pf} $的决定性理想，分别是亚Ximimail pffaffians的理想。我们使用通用线性群体的降文化和表示理论，我们扩展基于Raicu-Weyman-witt的工作，以确定$ s $ s-module结构的$ \ operatatOrName {ext}^j_s（s/i^t，s/i^t，s）$和$ \ operatateName {ext}这些$ \ operatorname {ext} $模块的发电机。结果，通过分级的本地二元性，我们回答了Wenliang Zhang在形式的本地共同体学模块的Socle学位上的问题，$ h^j_ \ mathfrak {m}（s/i^t）$。
Let $S$ be the polynomial ring on the space of non-square generic matrices or the space of odd-sized skew-symmetric matrices, and let $I$ be the determinantal ideal of maximal minors or $\operatorname{Pf}$ the ideal of sub-maximal Pfaffians, respectively. Using desingularizations and representation theory of the general linear group we expand upon work of Raicu--Weyman--Witt to determine the $S$-module structures of $\operatorname{Ext}^j_S(S/I^t, S)$ and $\operatorname{Ext}^j_S(S/\operatorname{Pf}^t, S)$, from which we get the degrees of generators of these $\operatorname{Ext}$ modules. As a consequence, via graded local duality we answer a question of Wenliang Zhang on the socle degrees of local cohomology modules of the form $H^j_\mathfrak{m}(S/I^t)$.
