Research on Characteristic Classes of Singular Varieties

单一品种特征类研究

基本信息

批准号：
11440014
负责人：
SUWA Tatsuo
金额：
$ 7.55万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

项目摘要

Directed by the head investigator Suwa, the research on characteristic of singular varieties, in particular the theory of Milnor classes and related topics have been performed, as described in the research proposal, We obtained an explicit formula for the Minor class of a non- singular component of singular variety, the notion of the homology Chern class is introduced. The Riemann-Roch theorem for embeddings of singular varieties are proved arid used to compute the Chern class of the tangent sheaf of a singular variety. As an application of the theory of localization of characteristic classes, we defined, for functions on singular varieties the notion of multiplicity at the singularity, gave the method to compute them and proved, in the global situation, the "multiplicity formula", which generalized well-known classical formula in the non-singular case. We also gave a direct and geometric proof of the Lefschetz fixed point formula for the de Rham and Dolbeault complexes.The other investigators collaborated in the above projects and also obtained many other results in the subjects such as : the moduli space of Abelian varieties, me McKay correspondence of simple singularities, developable surfaces of curves in the Euclidean space and classification of singularities of Dalboux sphere representations, stability of singular Lagrangian varieties, singular fibers of elliptic K3 surges and the torsion subgroup of the Mordell-Weli group, geometry of sextic curves of torus type and the geometry of dual curves, an alternative proof of the algebraic independence of the Monta-Mumfoixl classes, parital answer to the Akita conjecture on the mapping class group.

如研究提案所述，由首席研究员Suwa导演，有关奇异品种特征的研究，尤其是Milnor类和相关主题的理论，我们获得了一个明确的公式，用于引入奇异品种的非单数组成部分，即同源类别的概念Chern Chern Chern Chern类。事实证明，用于计算奇异品种的切线捆的Chern类别的Riemann-Roch定理被证明是干旱的。作为特征类别定位理论的应用，我们定义了在奇异品种上的函数，以奇异性的多样性概念进行了计算它们的方法，并在全球情况下证明了“多重性公式”，在非单明性情况下，该概述了概括性的经典公式。 We also gave a direct and geometric proof of the Lefschetz fixed point formula for the de Rham and Dolbeault complexes.The other investigators collaborated in the above projects and also obtained many other results in the subjects such as : the moduli space of Abelian varieties, me McKay correspondence of simple singularities, developable surfaces of curves in the Euclidean space and classification of singularities of Dalboux sphere表示，奇异品种的稳定性，椭圆形K3的奇异纤维以及Mordell-Weli组的扭转亚组，六曲线类型的六曲线几何形状以及双向曲线的几何形状，蒙塔（Monta-Mumfoixl Classe）的代数独立性的替代性证明了pare complate complate complate complate complate complate complate contaper conterage complate pareperty on parity paritage and paritaper and paritage and paritage noception paritage and parital paritame nocping the parital mopperty paritage。