论文标题
Macaulay二元性及其几何形状
Macaulay duality and its geometry
论文作者
论文摘要
峰值二元性，在多项式环上的字段的商之间，被变量的能力消灭，并在任何noetherian戒指上被概括，并在任何Noetherian戒指上概括，并用于在吉尔伯特方案的各个sperticals of Supere supere supere septers and supchem septers of Supere septers and conters and sane septers和相应的群体之间提供同构的同构。因此，值得注意的是，允许SOCLE类型的递归压缩代数的轨迹被开放的亚化学覆盖，每一个都与某个仿射空间的开放式子处理相同。此外，多项式变量是加权的，多项式环由分级模块取代，并将注意力集中在诱导的过滤和等级上。此外，为（相对）的gorenstein Artinian代数（相对）最大的商发展了类似的理论。
Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers of the variables, and finitely generated submodules of the ring's graded dual, is generalized over any Noetherian ring, and used to provide isomorphisms between the subschemes of the Hilbert scheme parameterizing various sorts of these quotients, and the corresponding subschemes of the Quot scheme of the dual. Thus notably the locus of recursively compressed algebras of permissible socle type is proved to be covered by open subschemes, each one isomorphic to an open subscheme of a certain affine space. Moreover, the polynomial variables are weighted, the polynomial ring is replaced by a graded module, and attention is paid to induced filtrations and gradings. Furthermore, a similar theory is developed for (relatively) maximal quotients of a graded Gorenstein Artinian algebra.
