Singularities in positive characteristic, stratification and simplification of the singular locus

By Ana Bravo, Orlando Villamayor. 2008

52 citations recorded by the source corpus.

Abstract We introduce an upper semi-continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic. The blow-up along the maximum stratum defined by this function leads to a form of simplification of the singularities, known as the reduction to the monomial case.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3fe6dc1d856aaf30cd26cbc78c8509250ec78d6d

How researchers see this paper

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In Geometry and Topology

1. Herwig Hauser
2. Steven Dale Cutkosky
3. J. Włodarczyk
4. Orlando Villamayor
5. Ana Bravo
6. Donghoon Hyeon
7. Brendan Hassett

In Mathematical Physics

1. Herwig Hauser

Citations in the corpus

• Resolution of singularities of arithmetical threefolds (2014, unknown): “Even when wild ramification occurs, this method induces some simplification from the general case and is the starting point of several approaches [14][79].”
• On the problem of resolution of singularities in positive characteristic (Or: A proof we are still waiting for) (2009, methodology): “There is a novel approach to resolution by Villamayor and his collaborators Benito, Bravo and Encinas [Vi2, Vi3, BV , EV3].”