A short note on Hauser's Kangaroo phenomena and weak maximal contact in higher dimensions

英文摘要：

Currently there are several approaches to resolution of singularities in positive characteristic all of which have hit some obstruction. One natural idea is to try to construct new meaningful examples at this point to gain a wider range of experience. To produce such examples we mimic the characteristic zero approach and focus on cases where it fails. In particular, this short note deals with an example-driven study of failure of maximal contact and the search for an appropriate replacement.