Residues on Singular Varieties

单一品种的残留

• 批准号: 15340016
• 负责人: SUWA Tatsuo
• 金额: $ 5.18万
• 依托单位: Niigata University (2005)Hokkaido University (2003-2004)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340016/
• 关键词: Singular varieties; Localization of characteristic classes; Residues; Chern classes; Local Euler obstructions; Holomorphic foliations; Complex dynamical systems; Intersection theory; 交点理論; 切断の組; Thom-Porteous公式

The head investigator and the others did research on residues on singular varieties. More specifically :1.We developed a theory of residues of Chern classes of vector bundles on singular varieties with respect to collections of sections. We also gave explicit expressions (analytic, algebraic and topological) of the residues at an isolated singular point.2.We introduced the notion of multiplicity for functions on singular varieties and proved a generalization of a formula of Iversen for holomorphic maps onto a Riemann surface.3.In the case of the top Chern class, the Thom class contains local informations and produces analytic., algebraic and topological invariants through the Bochner-Martinelli kernel. We found the "intermediate Thom classes" for other Chern classes.4.In a collaboration with J.-P.Brasselet and J.Seade, we proved a "proportionality theorem" for the local Euler obstruction of 1-forms on singular varieties.5.In a collaboration with F.Bracci, we prove the existence of parabolic curves at a fixed point of a holomorphic self-map of a singular complex surface, as an application of our residue theory. For this, we developed the intersection theory of curves in singular surfaces, using the Grothendieck residues on singular varieties.6.Besides the above, Ito obtained important results on the Poincare-Hopf type theorems, Ohmoto on the characteristic classes of algebraic stacks, Oka on the fundamental group of the complement of algebraic curves, Tajima on Milnor and Tjurina numbers, Yokuraon motivic characteristic classes, respectively.

首席调查员和其他人对奇异品种的残留物进行了研究。更具体地说：1。我们开发了一种关于奇异品种的Chern类别载体捆绑包的残基理论，相对于部分集合。我们还给出了一个孤立的奇异点的残留物的明确表达（分析，代数和拓扑）。2。我们引入了在奇异品种上的功能的多样性的概念，并证明了iversen公式的概括性的概括性，用于整体群体的综合型群体。通过Bochner-Martinelli内核不变。我们找到了其他Chern类的“中间班级”。4。在与J.-P. Brasselet和J.Seade的合作中，我们证明了当地的Euler障碍物在奇异品种上的1型障碍物的“相称性理论”。5。在与F.Bracci的合作中，我们证明了与Parabolic Curves Ane Serforce nefervence a holor n holor a holom and holom and holom and holom a hol sermosor a sermosor a seraportion的应用。残留理论。 For this, we developed the intersection theory of curves in singular surfaces, using the Grothendieck residues on singular varieties.6.Besides the above, Ito obtained important results on the Poincare-Hopf type theorems, Ohmoto on the characteristic classes of algebraic stacks, Oka on the fundamental group of the complement of algebraic curves, Tajima on Milnor and Tjurina数字，洋子动机特征类别。

项目成果

Classifying singular Legendre curves by contactomorphisms

通过接触同态对奇异勒让德曲线进行分类

• 发表时间: 2004
• 期刊: Journal of Geometry and Physics 52
• 作者: Y. Ebihara;Y. Miyoshi;K. Asamura;et al;S.Severmann et al.;G.Ishikawa
• 通讯作者: G.Ishikawa

T.Suwa: "Characteristic classes of singular varieties"Sugaku Expositions, A.M.S.. 16. 153-175 (2003)

T.Suwa：“奇异品种的特征类别”Sugaku Expositions，A.M.S.. 16. 153-175 (2003)

I.Shimada: "Fundamental groups of algebraic fiber spaces"Comment.Math.Helu.. 78. 335-362 (2003)

I.Shimada：“代数纤维空间的基本群”评论.Math.Helu.. 78. 335-362 (2003)

Supersingular K3 surfaces in odd characteristic and sextic double plane

奇特征和六重双平面中的超奇异 K3 表面

• 发表时间: 2004
• 期刊: Math.Ann. 328
• 作者: 大本 亨;T.Ohmoto;諏訪 立雄;伊藤 敏和;岡 睦雄;田島 慎一;與倉 昭治;T.Suwa;T.Ito;M.Oka;S.Tajima;S.Yokura;T.Suwa;I.Nakamura;G.Ishikawa;G.Ishikawa;I.Shimada;I.Shimada
• 通讯作者: I.Shimada

T.Suwa: "Multiplicities of functions on singular varieties"Intern.J.Math.. 14. 541-558 (2003)

T.Suwa：“奇异变体上函数的多重性”Intern.J.Math.. 14. 541-558 (2003)