Research on Dutta multiplicity and Roberts ring

Dutta重数和Roberts环的研究

基本信息

  • 批准号:
    12640032
  • 负责人:
  • 金额:
    $ 2.3万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    2000
  • 资助国家:
    日本
  • 起止时间:
    2000 至 2002
  • 项目状态:
    已结题

项目摘要

1. We proved that the positivity problem of intersection multiplicity had a deep relation with the positivity of Dutta multiplicity. The Dutta multiplicity of a complex is a rational number that was defined by Dutta in the case of positive characteristic. We defined the Dutta multiplicity without the assumption on the characteristic. Using Adams operation for complexes (due to Gillet-Soule), we succeeded to describe the Dutta multiplicity and prove the positivity in some special cases. We also gave another description of Dutta multiplicity without using K-theory.2. The key point of the proof of the vanishing of intersection multiplicity due to Roberts is the vanishing of Todd classes of local rings. The Todd classes of local rings are very interesting, but it is very difficult to calculate concrete examples. We succeeded to give an formula on Todd classes of local rings in some special cases. Using it, we calculate some examples. We found that there are many examples that satisfy the vanishing of Todd classes, we call such rings Roberts rings. We studied basic properties on Roberts rings.3. Flat morphisms of rings induces a map of Grothendieck groups. For a Northerian local ring, we studied a map between Grothendieck groups induced by the completion. More precisely, we studied when it is injective. We found some sufficient conditions for the injectivity. For example, it is injective if the given local ring is isolated singularity.
1. 证明了交多重性的正性问题与Dutta多重性的正性有很深的关系。复数的Dutta多重是一个有理数,是由Dutta在正特征的情况下定义的。我们在没有特征假设的情况下定义了Dutta多重性。利用复合体的Adams运算(由于Gillet-Soule),我们成功地描述了Dutta多重性,并在一些特殊情况下证明了其正性。我们还给出了不使用k理论的Dutta多重性的另一种描述。由Roberts引起的交多重性消失的证明的关键是局部环Todd类的消失。局部环的Todd类非常有趣,但是很难计算出具体的例子。在一些特殊情况下,我们成功地给出了局部环Todd类的一个公式。用它计算了一些例子。我们发现有很多例子满足Todd类的消失,我们称这种环为Roberts环。我们研究了罗伯茨环的基本性质。环的平面态射引出了Grothendieck群的图。对于一个northern局部环,我们研究了由补全引起的Grothendieck群之间的映射。更准确地说,我们研究了它什么时候是注入的。我们找到了注入性的几个充分条件。例如,如果给定的局部环是孤立奇点,则它是内射。

项目成果

期刊论文数量(26)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Y.Kamoi: "On maps of Grothendieck groups induced by completion"J.Alg.. 254. 21-43 (2002)
Y.Kamoi:“关于由完成引起的格洛腾迪克群的地图”J.Alg.. 254. 21-43 (2002)
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Kazuhiko Kurano: "The positivity of intersection multiplicities and symbolic powers of prime ideals"Compositio Math.. 122. 165-182 (2000)
Kazuhiko Kurano:“交叉多重性的正性和素理想的象征力量”Compositio Math.. 122. 165-182 (2000)
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Kazuhiko Kurano: "Todd classes of affine cones of Grassmannians"Int. Math. Res. Notices. 35. 1841-1855 (2002)
Kazuhiko Kurano:“格拉斯曼尼亚的仿射锥的托德类”Int。
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Kazuhiko Kurano: "Roberts rings and Dutta multiplicities"Lect. Notes in Pure and Applied Math. 217. 273-287 (2001)
Kazuhiko Kurano:“罗伯茨环和杜塔多重性”Lect。
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Hiroaki Terao: "Moduli space of combinatorially equivalent arrangements of hyperplanes and logarithmic Gauss-Manin connections"To appear in Topology and its appl..
Hiroaki Terao:“超平面和对数高斯-马宁连接的组合等效排列的模空间”出现在拓扑学及其应用中。
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KURANO Kazuhiko其他文献

KURANO Kazuhiko的其他文献

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{{ truncateString('KURANO Kazuhiko', 18)}}的其他基金

Study of local rings with discrete class group and its Picard number
离散类群局部环及其皮卡数研究
  • 批准号:
    21540050
  • 财政年份:
    2009
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
A research of algebraic cycles on local rings
局部环代数环的研究
  • 批准号:
    18540052
  • 财政年份:
    2006
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Numerical equivalence on Chow groups of local rings and its applications
局部环Chow群的数值等价及其应用
  • 批准号:
    15540038
  • 财政年份:
    2003
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Resolution of singularities in arbitrary characteristic
解决任意特征中的奇点
  • 批准号:
    10640035
  • 财政年份:
    1998
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)

相似海外基金

On the Grothendieck Group of a Finite Group
论有限群的格洛腾迪克群
  • 批准号:
    7701799
  • 财政年份:
    1977
  • 资助金额:
    $ 2.3万
  • 项目类别:
    Standard Grant
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