Mathematical Sciences: Normal Singularities

这个项目是关于正规奇点的结构和变种之间的映射的各种问题。主要研究者将确定完全理想的乘积是否具有有理表面奇点的特征。他将研究正规Cohen-Macauley变异体奇点的分辨，以及代数流形之间的两族映射的结构。研究了正特征面奇异局部基群的结构。这项工作是交换代数和代数几何的结合。研究者将检查与一个表面相关的代数结构，看看是否可以得到有关该表面的信息。这是目前数学中非常活跃的一个领域。

This project is concerned with various questions about the structure of normal singularities and of maps between varieties. The principal investigator will determine if the product of complete ideals being complete characterizes rational surface singularities. He will study the resolutions of singularities of a normal Cohen-Macauley variety as well as the structure of birational maps between algebraic manifolds. The structure of the local fundamental group of surface singularities in positive characteristic will be investigated. This work lies on the interface of commutative algebra and algebraic geometry. The investigator will examine algebraic structures associated with a surface to see if information can be derived concerning the surface. This is currently a very active area of mathematics.