Critical Points of Functions on Singular Spaces

Details Critical Points of Functions on Singular Spaces Critical Points of Functions on Singular Spaces

1999-08-19

arxiv.org/abs/math/9908104v1

Mathematics

Algebraic Geometry

35 pages

Scientific paper

We compare and contrast various notions of the "critical locus" of a complex
analytic function on a singular space. After choosing a topological variant as
our primary notion of the critical locus, we justify our choice by generalizing
L\^e and Saito's result that constant Milnor number implies that Thom's a_f
condition is satisfied.

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