Mathematical Sciences: Presidential Young Investigator

本研究的主旨是研究三维代数簇(三重)。首席研究者过去的工作将继续关于代数纤维空间的问题，以及在三重分类中的应用。目前的工作还涉及三重之间的二元映射的结构，特别是余维-两个代数运算被称为翻转和翻转，这现在被理解为三维二元映射的中心特征。所有这一切的一个潜在应用是通过研究从单参数曲面族得到的三重曲面的纤维，特别是该纤维的曲率性质，产生曲面的模空间的几何意义紧致。

The main thrust of this research is to study three dimensional algebraic varieties (threefolds). The Principal Investigator's past work will be continued on questions on algebraic fibre spaces together with the applications to the classification of threefolds. The current work also concerns the structure of birational mappings between threefolds, especially the codimension-two algebraic surgerys called "flips" and "flops" which are now understood to be a central feature of birational maps in dimension three. A potential application of all of this is to produce a geometrically meaningful compactification of moduli spaces of surfaces via the study of the fibration of the threefold obtained from a one-parameter family of surfaces, especially curvature properties of that fibration.