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

为了解决奇点的求解问题，这是代数几何中一个长期存在的开放性问题，作者开发了自己的程序IFP。他在IFP框架下定义了一个不变量，并证明了它在爆炸前的情况下表现得很好。此外，通过膨胀检验不变量的期望行为的性质，他发现了使用严格变换得到更好不变量的可能性，并得到了一些关于它的部分结果。

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.