Mathematical Sciences: Resolution of Singularities of an Algebraic Variety over a Field of Characteristic p.

这项建议中的研究涉及通过双态变换来消除(或解决)代数簇的奇点。23年前，平中在特征为零的情况下解决了这个问题。从那时起，特征p0的情况就抵制了所有的尝试。这一问题是本文研究的重点。在代数几何中，人们研究的许多几何对象都有奇点，即角或尖点。以某些规定的方式消除这些是一个非常重要的问题。这位首席研究员多年来在这个问题上有了第一个真正的新想法。如果他解决了这个问题，甚至在这方面取得了重大进展，那将是一个重大的进步。对于这种深度的问题，人们只能拭目以待。

The research in this proposal concerns the removing (or resolution of) singularities of an algebraic variety by birational transformations. This problem was solved 23 years ago by Hironaka in the case of characteristic zero. The case of characteristic p 0 has resisted all attempts since then. This problem is the focus of this research. In algebraic geometry many of the geometric objects one studies (varieties) have singularities, i.e. corners or cusps. It is a very important problem to remove these in certain prescribed ways. The principal investigator has the first really new idea on this problem in many years. If he solves this problem or even makes significant headway on it, it would be a significant advance. One can only wait and see on a problem of this depth.