Functorial flatification of proper morphisms
David Rydh
TL;DR
This paper introduces a functorial flatification algorithm for proper morphisms using blow-ups, extending Hironaka's method, and also presents an étalification algorithm via Kummer blow-ups in characteristic zero.
Contribution
It provides a new functorial flatification method for proper morphisms and an étalification algorithm in characteristic zero, advancing resolution techniques.
Findings
Functorial flatification by blow-ups for proper morphisms.
Flatification in characteristic zero using smooth centers.
Functorial étalification via Kummer blow-ups in characteristic zero.
Abstract
For proper morphisms, we give a functorial flatification algorithm by blow-ups in the spirit of Hironaka's flatification algorithm. In characteristic zero, this gives functorial flatification by blow-ups in smooth centers. We also give a functorial \'etalification algorithm by Kummer blow-ups in characteristic zero.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Digital Image Processing Techniques