Mathematical Sciences: Torsionfree Modules over Affine Coordinate Rings

本研究将考虑无扭的 仿射代数簇的坐标环上的模， 特别是表面和三折。 校长 研究人员将获得直接和抵消理论， 这些模块，并将其应用到具体的取消 问题 这将通过将所有 环上的不可分解双生成无挠模 只有有理双点作为奇点的曲面， 得到这些模的直和的不变量。 本研究是在交换代数的一般领域 涉及模块的结构理论， 取消问题。 这项工作是一个有趣的组合 从经典模理论和几何学的技巧。 的 将要研究的问题是深刻而重要的。 的 这个项目的结果将是感兴趣的数学 社区

This research will consider finitely generated torsionfree modules over coordinate rings of affine algebraic varieties, particularly surfaces and three-folds. The principal investigator will obtain a theory of direct-sum cancellation for these modules and will apply it to specific cancellation problems. This will be accomplished by classifying all indecomposable finitely generated torsionfree modules over surfaces with only rational double points as singularities and by obtaining invariants for direct sums of these modules. This research is in the general area of commutative algebra and is concerned with the structure theory of modules and cancellation problems. This work is an interesting combination of techniques from classical module theory and geometry. The questions that will be examined are deep and important. The outcome of this project will be of interest to the mathematical community.