Herwig Hauser

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This is the first of a series of papers related to resolution of singularities. We present here examples which explain why many arguments and proofs work in special situations, say small dimension or zero characteristic, but fail in general. This exhibits in particular the delicacy of resolution of singularity for arbitrary excellent schemes. The examples(More)
Purpose of the present paper is to reveal part of the beauty and delicacy of resolution of singularities in the case of excellent two-dimensional schemes embedded in three-space and defined over an algebraically closed field of arbitrary characteristic. The proof of strong embedded resolution we describe here combines arguments and techniques of O. Zariski,(More)
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In this paper we shall describe three techniques which allow to work efficiently with power series in various problems of singularity theory, especially in the context of resolution of singularities. The key problem in resolution of singularities is the construction of local invariants of singular schemes and their control under blowup and localization. Our(More)
Assume that, in the near future, someone can prove resolution of singularities in arbitrary characteristic and dimension. Then one may want to know why the case of positive characteristic is so much harder than the classical characteristic zero case. Our intention here is to provide this piece of information for people who are not necessarily working in the(More)
We present a method for the construction of solutions of certain systems of partial differential equations with polynomial and power series coefficients. For this purpose we introduce the concept of perfect differential operators. Within this framework we formulate division theorems for polynomials and power series. They in turn yield existence theorems for(More)
This is – for the time being – the last of a series of papers of the author on resolution of singularities. This series started with a collection of obstacles which make resolution in arbitrary dimension and characteristic difficult [Ha 1]. It was followed by a comprehensive study of Hironaka’s proposal for surface resolution in positive characteristic [Ha(More)
Wild singularities are the main obstacle for applying the characteristic zero proof of resolution of singularities to the case of characteristic p > 0. They cause at certain points of the exceptional divisor of blowups, so called kangaroo points, the increase of the resolution invariant. This increase destroys the induction argument. In the article, we(More)