Higher Dimensional Algebraic Varieties

该建议的目的是研究代数几何、拓扑学和数论之间的联系。具体而言，争论的焦点是变种拓扑学和Kodaira维度之间的关系。此外，该项目将研究变元的退化及其在求解局部域上的丢番图方程中的应用。这里的研究目的是提供关于哪些形状可以有效地用方程来描述的理论理解。这种形状包括曲线和曲面，但也包括更高维空间中的更高维形状。特别有趣的是对参数化形状的描述，因为这提供了用于计算目的的快速算法。

The purpose of the proposal is to study the connections between algebraic geometry, topology and number theory. Specifically, at issue is the relationship between thetopology of a variety and the Kodaira dimension. Furthermore,the project will investigate the degeneration of varietiesand their application to solving diophantine equations overlocal fields.The aim of the research here is to furnish a theoreticalunderstanding about which shapes can be describedefficiently with equations. Such shapes include curves and surfaces but alsohigher dimensional shapes in higher dimensional spaces. Of specialinterest is a description of parametrized shapes, since this provides fast algorithms for computational purposes.