Mathematical Sciences: Some Natural Problems in Complex Geometry

首席研究员将研究几个困难的 复杂几何问题。 在证明了一个基本的 初步结果，PI现在将找到一套完整的 复超曲面族的连续不变量。 这个问题可以归结为研究低维的 用代数方法。 PI还将研究 具有真实的的复子流形的同构类 余维大于3。他会用他的理解力 的Kohn-Rossi上同调，以解决复杂的高原 问题. 拟议中的工作将阐明复杂的 高原问题和我们对超曲面的理解， 包含在高维复杂空间中。 等 这些问题起源于高斯最初的研究， 虚数，如-1的平方根。

The principal investigator will study several difficult problems in complex geometry. Having proved a fundamental preliminary result, the PI will now find a complete set of continuous invariants for families of complex hypersurfaces. This problem may be reduced to studing the lower dimensional case by algebraic means. The PI will also study the diffeomorphism classes of complex submanifolds with real codimension greater than three. He will use his understanding of the Kohn-Rossi cohomology to solve the complex Plateau problem. The proposed work will shed light on the difficult complex Plateau problem and on our understanding of hypersurfaces which are contained in high dimensional complex spaces. Such problems have their origins in Gauss's original studies of imaginary numbers such as the square root of -1.