We give the description of an algorithm for the resolution of singularities, in the case of hypersurfaces in characteristic zero, based on Villamayor's stratifying function. The algorithm is implemented in Maple.
Algebraic varieties that are locally isomorphic to open subsets of affine space will be called plain. Plain varieties are smooth and rational. The converse is true for curves and surfaces, and is unknown in general. It is shown that plain varieties are stable under blowup in smooth centers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.