Resolution of Singularities of an algebraic varieties defined over an algebraically closed field

为了解决代数几何中一个长期悬而未决的问题--奇点分解问题，作者开发了自己的程序，称为IFP。他在IFP框架中定义了一个消解不变量，并证明了它在爆炸前的情况下表现得很好。此外，通过研究爆破不变量的预期行为的性质，他发现了使用严格变换得到更好的不变量的可能性，并得到了与之相关的一些部分结果。

To solve the problem of resolution of singularities, a longstanding open problem in algebraic geometry, the author developed his own program, called IFP. He defined an invariant for resolution in the framework of IFP, and show that it behaves quite well in the situation before blowups. Moreover, by examining the properties for the expected behavior of invariants through blowups, he found the possibility of the better invariant using strict transforms, and obtained some partial results concerning it.