Resolving Surface Singularities in Positive Characteristic
Year: 2024
Type: article
Abstract: The paper contains a systematic proof for the embedded resolution of two-dimensional hypersurface singularities over a field of arbitrary characteristic. It relies on the construction of a local upper semicontinuous invariant whose top locus defines at each stage of the resolution process the center of a permissible blowup under which the invariant improves. As the invariant belongs to a well-ordered set, resolution is achieved in finitely many steps. To define the invariant we analyze in detail the obstructions which occur when transcribing the inductive characteristic zero proof à la Hironaka. These difficulties are then overcome by introducing finer invariants than in zero characteristic: They reflect and control typical characteristic p phenomena. This may give new ideas for approaching the characteristic p resolution in higher dimensions.
DOI: 10.4171/prims/60-4-5
Authors: Herwig Hauser, Stefan Perlega
Institution: University of Vienna
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4404143002