The critical curvature degree of an algebraic variety

In this article we study the complexity involved in the computation of the reach in arbitrary dimension and in particular the computation of the critical spherical curvature points of an arbitrary algebraic variety. We present properties of the critical spherical curvature points as well as an algorithm for computing them.& COPY; 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by-nc -nd /4 .0/).

Automated summary

In this article, we explore the complexity involved in computing reach in arbitrary dimension and specifically the critical spherical curvature points of an arbitrary algebraic variety. We present the properties of these critical points and introduce an algorithm for their computation.