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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.

近几十年来，代数簇的研究一直十分活跃。不仅代数簇本身，而且代数簇上结构的可育性也吸引着代数和几何学者。此外，从共形场论和卡-丘流形的研究中可以看出，它与包括物理学在内的各个领域的关系越来越密切。本课题关注群在代数簇上的作用、Hodge理论与Kahler流形的周期映射、代数簇上的各种模空间、算术簇上的共形场论、K-理论与数论之间的相互关系，力求在代数簇的研究方面取得较大进展，除了研究者的个人研究外，我们组织了多次会议，设计了相关领域之间的密切交流，并派项目成员参加了相关会议，取得了以下良好的效果：抛物稳定层的模空间的构造及其结构的研究与应用，关于可能是奇异的投射方案的稳定层的模空间的构造，从数学观点的共形场论，卡-丘流形的构造、变形和镜像对称，模型-韦尔格的发展和应用，K3曲面的研究与应用，一般型曲面的存在性问题，Mori理论的发展。