Algebra and Geometry on Algebraic Varieties

代数簇的代数和几何

基本信息

批准号：
04302003
负责人：
MARUYAMA Masaki
金额：
$ 12.35万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1992
资助国家：
日本
起止时间：
1992 至 1994
项目状态：
已结题

项目摘要

In the last few decades the study on algebraic varieties has been very active. Not only algebraic varieties itself but also the fertility of the structures over algebraic varieties are attracting the scholars of algebra and geometry. Moreover, as we can see in the research of the conformal field theory and the Calabi-Yau manifolds, the relationship with various fields including physics is getting closer. In this project, paying attention to the interrelation among actions of groups on algebraic varieties, Hodge theory and period maps of Kahler manifolds, various moduli spaces on algebraic varieties, conformal field theory on arithmetic varieties, K-theory and number theory, we tried to make great progress in studying algebraic variety, In addition to individual studies in the neighborhoods of investigators, we organized several conferences to design close communication between related fields and sent members of the project to relevant conferences.We could get the following excellent results : construction of the moduli space of parabolic stable sheaves, study and applications of its structure, construction of the moduli space of stable sheaves on prejective schemes that may be singular, conformal field theory from the mathematical viewpoint, constructions, deformations and mirror symmetries of Calabi-Yau manifolds, development and applications of Model-Weil lattices, study and applications of K3 surfaces, existence prpblem of the surfaces of general type, development of Mori theory.

在过去的几十年中，关于代数品种的研究非常活跃。不仅代数品种本身，而且在代数品种上的结构的生育能力吸引了代数和几何学学者。此外，正如我们在保形场理论和卡拉比河流形的研究中所看到的那样，与包括物理在内的各种领域的关系越来越近。在这个项目中，请注意小组对代数品种的行动，霍奇理论和卡勒流形的周期地图，关于代数品种的各种模态空间，关于算术品种，k-bewor和数字理论的共同领域理论，我们试图在研究范围内取得了巨大的进展，并在研究范围内取得了巨大的进步。 communication between related fields and sent members of the project to relevant conferences.We could get the following excellent results : construction of the moduli space of parabolic stable sheaves, study and applications of its structure, construction of the moduli space of stable sheaves on prejective schemes that may be singular, conformal field theory from the mathematical viewpoint, constructions, deformations and mirror symmetries of Calabi-Yau manifolds, development and applications of模型 - 韦尔晶格，K3表面的研究和应用，一般类型表面的存在，莫里理论的发展。