In algebraic geometry, an equisingularity is, roughly, a family of singularities that are not non-equivalent and is an important notion in
singularity theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...
. There is no universal definition of equisingularity but Zariki's equisingularity is the most famous one. Zariski's equisingualrity, introduced in 1971 under the name " algebro-geometric equisingularity", gives a stratification that is different from the usual
Whitney stratification In differential topology, a branch of mathematics, the Whitney conditions are conditions on a pair of submanifolds of a manifold introduced by Hassler Whitney in 1965.
A stratification of a topological space is a finite filtration by closed sub ...
on a real or complex algebraic variety.
See also
*
stratified space
In mathematics, especially in topology, a stratified space is a topological space that admits or is equipped with a stratification, a decomposition into subspaces, which are nice in some sense (e.g., smooth or flat).
A basic example is a subset o ...
References
Further reading
*https://mathoverflow.net/questions/299314/a-general-definition-of-an-equisingular-family-of-singular-varieties
algebraic geometry
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