arXiv subjects

Anne Fruehbis-Krueger

Publications and source records attributed to Anne Fruehbis-Krueger.

4 recordsLinked to original sources

arXiv2020

Embedded desingularization for arithmetic surfaces -- toward a parallel implementation

We present an algorithmic embedded desingularization of arithmetic surfaces bearing in mind implementability. Our algorithm is based on work by Cossart-Jannsen-Saito, though our variant uses a refinement of the order instead of the Hilbert-Samuel function as a measure for the complexity of the singularity. We particularly focus on aspects arising when working in mixed characteristics. Furthermore, we exploit the algorithm's natural parallel structure rephrasing it in terms of Petri nets for use in the parallelization environment GPI-Space with {\sc Singular} as computational back-end.

math.AG↗

arXiv2016

On the Vanishing Topology of Isolated Cohen-Macaulay Codimension 2 Singularities

Isolated Cohen-Macaulay codimension 2 singularities share many common features with isolated complete intersection singularities, but they also exhibit some striking new behaviour. One such instance was recently observed by Damon and Pike in their study of the vanishing topology and Euler characteristic, where they took this class of singularities as examples. In this article, we explore their findings further by determining the Betti numbers explicitly and explain the new phenomena. An important tool here is the Tjurina modification relating a Cohen-Macaulay codimension 2 singularity to a finite number of complete intersection singularities.

math.AG↗

arXiv2010

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

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.

math.AG↗

arXiv2008

Simple Cohen-Macaulay Codimension 2 Singularities

In this article, we provide a complete list of simple Cohen-Macaulay codimension 2 singularities together with a list of adjacencies which is complete in the case of fat point and space curve singularities.

math.AG↗