A canonical stratification

Immanuel Halupczok
Heinrich-Heine-Universität Düsseldorf

Date(s) : 10/06/2021   iCal
14 h 00 min - 15 h 00 min

A stratification of an algebraic set X ⊂ ℂ^n (or ℝ^n) is supposed to capture “how singular” the different points of X are: If x ∈ X lies in a stratum S, then there should exist a neighbourhood of x on which X is roughly translation invariant along S. This intuitive idea can be made precise if one replaces ℂ (or ℝ) by a bigger field K containing infinitesimal elements. Using this approach, we will construct an entirely canonical stratification of X. A motivation for this was to get a better control of the local Poincaré series associated to singularities of X. We will see how the canonical stratification indeed provides some control (though there are also questions that are still open). This is work in progress with David Bradley-Williams.


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