U.S.-Japan Cooperative Research: Joint Research in Higher- Dimensional Geometry

该奖项将使C教授。赫伯特克莱门斯和他的同事 犹他州大学与名古屋的森茂文教授合作 日本大学，为期两年。 他们将调查 高维几何的某些方面，特别是 三重曲线可缩性的上同调准则 三维K-平凡三重有理曲线的存在性 翻转;以及结果扩展到大于三的维度。 这些问题，除其他要考虑的问题外，都包括代数， 分析和拓扑方面，拟议的研究带来了 聚集了所有这些领域的专家。 这项研究的目的是增加我们对 三维或更多维的几何学。 为此日本 调查人员和同事将使用以下方法继续调查提出的问题： 增厚方法和翻转猜想，而美国组 将使用奇点的变形理论和霍奇理论。 预计这项工作将在该领域产生重要影响 在数学中，也是在研究变形的过程中， 材料的表面。

This award will enable Prof. C. Herbert Clemens and colleagues of the University of Utah to collaborate with Prof. Shigefumi Mori of Nagoya University, Japan, over a period of two years. They will investigate certain aspects of higher-dimensional geometry, in particular the cohomological criteria for contractibility of curves on threefolds; the existence of rational curves on K-trivial threefolds; 3-dimensional flips; and extensions of results to dimensions greater than three. These problems, among others to be considered, all comprise algebraic, analytic, and topological aspects, and the proposed research brings together experts in all of these fields. The purpose of this research is to increase our understanding of geometry in three and more dimensions. To this end, the Japanese investigator and co-workers will pursue the questions raised using the thickening method and the flip conjecture, while the U.S. group will use the deformation theory of singularities, and Hodge theory. This work may be expected to have important implications in the field of mathematics, and also in the study of the deformation of the surfaces of materials.