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Relative conormal spaces. I: Transversality conditions. (Espaces conormaux relatifs. I: Conditions de transversalité.) (French) Zbl 0888.32016
Let \(I=\langle f_1, \dots, f_m\rangle \subseteq\mathbb{C} \{x_1, \dots, x_n\}\) complete intersection ideal and consider the map \(f=(f_1, \dots, f_m): \mathbb{C}^n \to\mathbb{C}^m\).
The following transversality condition is introduced: for any two disjoint subsets of \(\{f_1, \dots, f_m\}\) the relative associated conormal spaces intersect only along the zero section of the cotangent space. It is proved that this condition is equivalent to a condition of Sabbah: \(f\) has no blowing-up in codimension zero, and the critical local of \(f\) is included in the union of zero locus of \(I\).
This can be applied to obtain some properties for differential modules associated to \(f\).

MSC:
32S05 Local complex singularities
14B05 Singularities in algebraic geometry
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