#### Filter Results:

- Full text PDF available (36)

#### Publication Year

1992

2017

- This year (2)
- Last 5 years (9)
- Last 10 years (24)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

Hironaka's spectacular proof of resolution of singularities is built on a multiple and intricate induction argument. It is so involved that only few people could really understand it. The constructive proofs given later by Villamayor, Bierstone-Milman and Encinas-Villamayor presented important steps towards a better understanding of the reasoning. They… (More)

- Herwig Hauser
- 1997

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)

- Herwig Hauser
- 2007

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)

- DE L’I.H.É.S, Herwig Hauser, Gerd K. Müller
- 2003

© Publications mathématiques de l’I.H.É.S., 1994, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://www. ihes.fr/IHES/Publications/Publications.html), implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression… (More)

- Herwig Hauser, Daniel Swarovski
- 2003

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)

- Herwig Hauser
- 2009

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)

- Sebastian Gann, Herwig Hauser
- J. Symb. Comput.
- 2005

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)

- Herwig Hauser
- 2003

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)

- Herwig Hauser
- 2008

In September 2008, Heisuke Hironaka gave a series of lectures at the Clay Mathematics Institute explaining his program for the resolution of singularities in positive characteristic [Hi1]. In the course of the lectures, Hironaka relied on results of the author from an unpublished manuscript written in 2003 [Ha1]. The quoted results investigate the main… (More)

- Herwig Hauser
- 2010

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)