Reduction Numbers and Multiplicities of Multigraded Structures-猫眼课题宝

多级结构的约简数和重数

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1997

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M. Herrmann;Eero Hyry;J. Ribbe;Zhongming Tang

该文致力于研究两个问题.首先，我们要把联系起来。Cohen] R I的麦考利性质，. . .，I to the Cohen]麦考利propA 1 r.。一般Rees环Rijs 1，. . .，R .然后，我们确定了Aj的重数，并构造了环.特别地，我们要问的是最小多重性何时出现。。。因为我？s I s I是多Rees代数R I s R I，. . .，I 1 r A r A。在某种程度上表现为普通的Rees代数RI。特别地，这类多Rees代数的Cohen]Macaulay性质可以用形式为的局部上同调的条件来刻画。我...我...环gr Ⅰ包含条件a gr Ⅰ 0，其中a gr Ⅰ表示A A A. w x。gr I的a-不变量见HHR 1。a-不变量在某个A中有。η w例中与理想I的约化指数r I有关见T2，x。。生长激素。此外，R I的Cohen]Macaulay性质隐含着A的Cohen] Macaulay性质。w x。R I为所有r）1。一般情况下，匡威则不成立，参见HHR 1。但是，A r。在某些应用中，假设R I是Cohen]Macaulay可以是A

The aim of this paper is twofold. First we want to relate the Ž . Cohen]Macaulay property of R I , . . . , I to the Cohen]Macaulay propA 1 r Ž . Ž . erty of the ordinary Rees rings R I j s 1, . . . , r . Then we determine A j the multiplicities of multi-Rees and form rings. In particular, we ask when minimal multiplicity occurs. Ž . Ž . For I s ??? s I s I the multi-Rees algebras R I s R I, . . . , I 1 r A r A Ž . behave to some extent like the ordinary Rees algebras R I . In particuA lar, the Cohen]Macaulay property of such multi-Rees algebras can be characterized in terms of conditions on the local cohomology of the form Ž . Ž Ž .. Ž Ž .. ring gr I including the condition a gr I 0, where a gr I denotes A A A Ž . Ž w x. the a-invariant of gr I see HHR 1 . The a-invariant has in certain A Ž . Ž w cases been related to the reduction exponent r I of the ideal I see T2, x. Ž . GH . Moreover, the Cohen]Macaulay property of R I implies that of A Ž . Ž w x. R I for all r ) 1. The converse is not true in general see HHR1 . But A r Ž . in certain applications the assumption R I is Cohen]Macaulay can be A

Reduction Numbers and Multiplicities of Multigraded Structures

多级结构的约简数和重数

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