Mathematical Sciences: Normal Singularities

这个项目涉及关于法线奇点和变种之间映射的结构的各种问题。首席研究者将确定完备理想的乘积是否刻画了有理曲面奇点的特征。他将研究正规Cohen-Macauley簇的奇点的分辨率以及代数流形之间的双态映射的结构。我们将研究正特征曲面奇点的局部基本群的结构。这项工作是在交换代数和代数几何的界面上进行的。研究人员将检查与表面相关的代数结构，看看是否可以得到关于该表面的信息。这是目前数学中一个非常活跃的领域。

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.