Study of Rees algebras and form rings

我想做的工作是从分次环的相应性质的角度研究与Noether局部环中理想相关联的Rees代数的某些环结构（如Buchsbaumness，Cohen-Macaulayness或Gorensteinness）.在[G1]中，我利用Cohen-Macaulay局部环（A，m）中m-极小重准素理想所对应的分次环和广义Rees代数的相应性质，给出了它们是Buchsbauxn环的一个刻划。作为这项研究的副产品，我构造了一个反例的负a-不变猜想所提出的Korb-Nakamura，有关的问题的Cohen-Macaulay在Rees代数。我给了一个讲座的例子在国际会议上交换代数在荣誉的大卫布克斯鲍姆（第三期，热那亚）在意大利（[G2]）。K.Yarnagishi [Y]推广了[G1]中的技巧，并利用Buchsbaum不变量给出了Buchsbaum局部环中m-准素理想的伴随分次环是Buchsbaum的一个显著的判别准则.他谈了这个标准在国际会议上交换代数在荣誉的大卫布克斯鲍姆（第一期，卡塔尼亚）在意大利，我组织的组织者之一。我也对非交换代数感兴趣，并与西田健二进行了联合研究。一些结果将出现在[GN1，GN2]中。

What I want to do in my research is to study certain ring-structures (such as Buchsbaumness, Cohen-Macaulayness, or Gorensteinness) of Rees algebras associated to ideals in Noetherian local rings, from the view-point of the corresponding properties of their associated graded rings. In [G1] I gave a characterization for the Rees algebras associated to m-primary ideals of minimal multiplicity in Cohen-Macaulay local rings (A, m) to be Buchsbauxn rings, in terms of the corresponding property of the associated graded rings and the extended Rees algebras as well. As a byproduct of this research I constructed a counterexample to the negative a-invariant conjecture raised by Korb-Nakamura, concerning a question on the Cohen-Macaulayness in Rees algebras. Igave a lecture about the examples in the International Conference on Commutative Algebra in honor of David Buchsbaum (the third period, Genova) in Italy ([G2]). Also, K.Yarnagishi [Y] generalized the techniques in [G1], and gave a striking criterion for the associated graded rings of m-primary ideals in Buchsbaum local rings to be Buchsbaum, in terms of the Buchsbaum invariant. He gave a talk about this criterion at the International Conference on Commutative Algebra in honor of David Buchsbaum (the first period, Catania) in Italy, which I organized as one of the organizers. I am also interested in non-commutative algebra and performed ajoint research with Kenji Nishida. Someof the results will appear in [GN1, GN2].